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root(3)(8y^(27))
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
2y^(3)
(B)
2y^(9)
(C)
(8)/(3)y^(3)
(D)
(8)/(3)y^(9)

$\sqrt[3]{8 y^{27}}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2 y^{3}$ $\newline$ (B) $2 y^{9}$ $\newline$ (C) $\frac{8}{3} y^{3}$ $\newline$ (D) $\frac{8}{3} y^{9}$

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Complete addition and subtraction equations with integers

Full solution

Q.

\sqrt[3]{8 y^{27}}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

2 y^{3}

\newline

(B)

2 y^{9}

\newline

(C)

\frac{8}{3} y^{3}

\newline

(D)

\frac{8}{3} y^{9}

Write expression in form: The given expression is the cube root of $8y^{27}$ , which can be written as $(8y^{27})^{\frac{1}{3}}$ .
Separate into product: We can separate the cube root of the product into the product of the cube roots: $(8)^{\frac{1}{3}} \times (y^{27})^{\frac{1}{3}}$ .
Calculate cube root of $8$ : The cube root of $8$ is $2$ , because $2^3 = 8$ . So, $(8)^{1/3} = 2$ .
Apply power rule of exponents: For the term $(y^{27})^{1/3}$ , we apply the power rule of exponents $(a^{m/n} = (a^m)^{1/n})$ , which gives us $y^{27/3}$ .
Simplify exponent: Simplifying $y^{\frac{27}{3}}$ gives us $y^9$ , because $27$ divided by $3$ is $9$ .
Multiply results: Multiplying the results from the previous steps, we get $2 \times y^9$ , which is $2y^9$ .

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