Select the equivalent expression. (a^(-2)*8^(7))^(2)=? Choose 1 answer: (A) (8a)^(10) (B) a^(-4)*8^(14) (c) 8^(9)

Apply product rule: Apply the power of a product rule, which states that (xy)^n = x^n * y^n, to the given expression (a^(-2)*8^(7))^(2).Raise factors to power of 2: Raise each factor inside the parentheses to the power of 2: (a^(-2))^2 and (8^(7))^2.Calculate new exponents: Calculate the new exponents by multiplying the exponents: (-2)*2 = -4 and 7*2 = 14.Write expression with new exponents: Write down the expression with the new exponents: a^(-4)*8^(14).Compare with choices: Compare the result with the given choices to select the correct answer.

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Select the equivalent expression.

(a^(-2)*8^(7))^(2)=?
Choose 1 answer:
(A)
(8a)^(10)
(B)
a^(-4)*8^(14)
(c)
8^(9)

Select the equivalent expression. $\newline$ $(a^{-2}\cdot 8^{7})^{2}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $(8a)^{10}$ $\newline$ (B) $a^{-4}\cdot 8^{14}$ $\newline$ (C) $8^{9}$

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(a^{-2}\cdot 8^{7})^{2}=

\newline

Choose

1

answer:

\newline

(A)

(8a)^{10}

\newline

(B)

a^{-4}\cdot 8^{14}

\newline

(C)

8^{9}

Apply product rule: Apply the power of a product rule, which states that $(xy)^n = x^n * y^n$ , to the given expression $(a^{-2} \cdot 8^{7})^{2}$
Raise factors to power of $2$ : Raise each factor inside the parentheses to the power of $2$ : $(a^{-2})^2$ and $(8^{7})^2$ .
Calculate new exponents: Calculate the new exponents by multiplying the exponents: $(-2) \times 2 = -4$ and $7 \times 2 = 14$ .
Write expression with new exponents: Write down the expression with the new exponents: $a^{-4} \cdot 8^{14}$ .
Compare with choices: Compare the result with the given choices to select the correct answer.