Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expressions are equivalent to
7^(-2)*7^(6) ?
Choose
2 answers:
A
(7^(2))/(7^(-2))
B
(7^(6))/(7^(-2))
c
7^(-12)
D
(7^(2))^(2)

Which expressions are equivalent to $\newline$ $7^{-2} \cdot 7^{6}$ ? $\newline$ Choose $\newline$ $2$ answers: $\newline$ A $\newline$ $\frac{7^{2}}{7^{-2}}$ $\newline$ B $\newline$ $\frac{7^{6}}{7^{-2}}$ $\newline$ C $\newline$ $7^{-12}$ $\newline$ D $\newline$ $(7^{2})^{2}$

View step-by-step help

View step-by-step help

Evaluate expressions using properties of exponents

Full solution

Q. Which expressions are equivalent to

\newline

7^{-2} \cdot 7^{6}

?

\newline

Choose

\newline

2

answers:

\newline

A

\newline

\frac{7^{2}}{7^{-2}}

\newline

B

\newline

\frac{7^{6}}{7^{-2}}

\newline

C

\newline

7^{-12}

\newline

D

\newline

(7^{2})^{2}

Simplify using properties of exponents: Simplify the expression using the properties of exponents. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $7^{-2}\times7^{6} = 7^{-2+6} = 7^{4}$
Compare to answer choices: Compare the simplified expression to the answer choices. $\newline$ We have simplified the expression to $7^{4}$ . Now we need to determine which of the given choices are equivalent to this expression. $\newline$ A) $(7^{2})/(7^{-2}) = 7^{2 - (-2)} = 7^{2 + 2} = 7^{4}$ $\newline$ B) $(7^{6})/(7^{-2}) = 7^{6 - (-2)} = 7^{6 + 2} = 7^{8}$ $\newline$ C) $7^{-12}$ is not equivalent to $7^{4}$ because the exponents are different. $\newline$ D) $(7^{2})^{2} = 7^{2*2} = 7^{4}$ $\newline$ Choices A and D are equivalent to $7^{4}$ .

More problems from Evaluate expressions using properties of exponents

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 3 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 3 months ago

Question

x^2 = 4

Posted 2 months ago

Question

x^2 = 9

Posted 4 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 4 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 4 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 4 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 15 days ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 2 months ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 2 months ago