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Resources

Simplify exponential expressions using the multiplication and division rules

Factor the trinomial.

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8x^{2}-5x+5y+24y^{2}

Simplify. Express your answer using positive exponents.

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\frac{8j^8}{4j^3 \cdot j^3}

Simplify. Express your answer using positive exponents.

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(4z^4)(4z^4)(10z^2)

Simplify. Express your answer using positive exponents.

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(6j)(8j)(6j^9)

Simplify. Express your answer using positive exponents.

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\frac{10b^7}{5b \cdot b^6}

Simplify. Express your answer using positive exponents.

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(7u)(2u)(5u^4)

Simplify. Express your answer using positive exponents.

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\frac{8j^5}{(8j^6)(j)}

Simplify. Express your answer using positive exponents.

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(4s^2)(4s^7)(3s^6)

Simplify. Express your answer using positive exponents.

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\frac{2z^2}{(2z^9)(z^6)}

Simplify. Express your answer using positive exponents.

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\frac{2y^7}{2y \cdot y^8}

Simplify. Express your answer using positive exponents.

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\frac{3p}{(3p^9)(p^8)}

Simplify. Express your answer using positive exponents.

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\frac{9 p^{6}}{9 p^{8} \cdot p^{4}}

\frac{4}{m}=8

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Multiply and remove all perfect squares from inside the square roots. Assume

b

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\sqrt{24 b^{3}} \cdot \sqrt{40 b^{2}} \cdot \sqrt{b^{2}}=

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\square

1

\frac{-3}{5}

as a rational number with denominator.

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20

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-30

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35

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-40

5

4

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5

4

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Simplify. Express your answer using positive exponents.

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(6 p q)\left(2 p^{5} q^{7}\right)

Use exponent laws to simplify

(\sqrt[8]{x})\left(\sqrt[5]{x^{3}}\right)

Simplify. Write your answer using whole numbers and variables.

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\frac{5n^2 - 3n}{5n - 3}

Simplify. Write your answer using whole numbers and variables.

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\frac{13p + 26}{p + 2}

Simplify by combining like terms.

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21 b-32+7 b-20 b-20

18

Multiply and divide powers: variable bases

85

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Simplify. Express your answer using positive exponents.

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7 u^{9} \cdot 2 u^{2} \cdot 7 u

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Simplify. Express your answer using positive exponents.

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\frac{7p}{7p}

Simplify. Express your answer using positive exponents.

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\frac{4z}{4z}

Example Question Using Covariance Formula

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Question: The table below describes the rate of economic growth (xi) and the rate of return on the S\&P

500\left(y_{i}\right)

. Using the covariance formula, determine whether economic growth and S\&P

500

returns have a positive or inverse relationship. Before you compute the covariance, calculate the mean of

x

y

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\begin{tabular}{|l|l|}

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\hline \begin{tabular}{l}

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Economic Growth \% \\

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\left(x_{i}\right)

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\end{tabular} & \begin{tabular}{l}

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500

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\left(y_{i}\right)

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\end{tabular} \\

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2

1

8

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2

5

12

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4

0

14

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3

6

10

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x=2.1,2.5,4.0

3

6

(economic growth)

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y=8,12,14

10

500

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\bar{x}

\bar{y}

Select all of the equations below that are equivalent to:

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pq = 11

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Use properties of equality.

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Multi-select Choices:

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9 + pq = 20

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4 + pq = 15

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pq + 7 = 18

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2 + pq = 13

Select all of the equations below that are equivalent to:

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12g = 8

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Use properties of equality.

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Multi-select Choices:

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12g - 3 = 4

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12g - 2 = 7

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12g - 3 = 5

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12g - 4 = 2

Select all of the equations below that are equivalent to:

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rs = 22

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Use properties of equality.

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Multi-select Choices:

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\frac{rs}{11} = 2

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\frac{rs}{11} = 4

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\frac{rs}{-11} = -3

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\frac{rs}{2} = 11

Select all of the equations below that are equivalent to:

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fg = 8

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Use properties of equality.

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Multi-select Choices:

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10 + fg = 18

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fg + 3 = 11

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fg + 4 = 12

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12 + fg = 20

Select all of the equations below that are equivalent to:

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3 + h = 7

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Use properties of equality.

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Multi-select Choices:

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3 + h + 10 = 15

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3 + h + 3 = 10

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14 + h = 12 + 7

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8 + h = 4 + 7

Simplify. Express your answer using positive exponents.

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\frac{6y}{(2y)(y^5)}

Simplify. Express your answer using positive exponents.

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\frac{6s}{(3s)(s^2)}

Simplify. Express your answer using positive exponents.

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\frac{9a^6}{a^3 \cdot 3a}

Simplify. Express your answer using positive exponents.

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\frac{6f^3}{2f \cdot f^3}

Simplify. Express your answer using positive exponents.

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\frac{3h}{(3h)(h^7)}

Simplify. Express your answer using positive exponents.

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\frac{7w}{w^7 \cdot 7w}

Simplify. Express your answer using positive exponents.

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\frac{9u^4}{(u)(3u)}

Simplify. Express your answer using positive exponents.

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(4t)(10t)(7t)

Simplify. Express your answer using positive exponents.

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\frac{5n^8}{(5n^4)(n^9)}

Simplify. Express your answer using positive exponents.

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\frac{6y^4}{2y^4 \cdot y^8}

Simplify. Express your answer using positive exponents.

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\frac{4k^2}{(2k^5)(k)}

Simplify. Express your answer using positive exponents.

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\frac{5n^7}{5n \cdot n}

Simplify. Express your answer using positive exponents.

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\frac{9s^2}{3s \cdot s}

Simplify. Express your answer using positive exponents.

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(9q)(5q)(6q^7)

Simplify. Express your answer using positive exponents.

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(7z^7)(9z^2)(5z^4)

Simplify. Express your answer using positive exponents.

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(8t)(5t)(5t)

Simplify. Express your answer using positive exponents.

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(8j)(9j)(4j)

Simplify. Express your answer using positive exponents.

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(10n)(6n)(9n^4)

Simplify. Express your answer using positive exponents.

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(6w)(2w)(8w^4)