Select the equivalent expression. (x^(-3)*y^(3))^(-7)=? Choose 1 answer: (A) x^(21)*y^(-21) (B) (xy)^(0) (C) x^(-10)*y^(-4)

Apply product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the expression (x^(-3)*y^(3))^(-7). (x^(-3)*y^(3))^(-7) = x^(-3 * -7) * y^(3 * -7)Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. x^(-3 * -7) * y^(3 * -7) = x^(21) * y^(-21)Check answer choices: Check the answer choices to see which one matches the simplified expression. The expression x^(21) * y^(-21) matches answer choice (A).

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Select the equivalent expression.

(x^(-3)*y^(3))^(-7)=?
Choose 1 answer:
(A)
x^(21)*y^(-21)
(B)
(xy)^(0)
(C)
x^(-10)*y^(-4)

Select the equivalent expression. $\newline$ $(x^{-3}y^{3})^{-7}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $x^{21}y^{-21}$ $\newline$ (B) $\newline$ $(xy)^{0}$ $\newline$ (C) $\newline$ $x^{-10}y^{-4}$

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(x^{-3}y^{3})^{-7}=

\newline

Choose

1

answer:

\newline

(A)

\newline

x^{21}y^{-21}

\newline

(B)

\newline

(xy)^{0}

\newline

(C)

\newline

x^{-10}y^{-4}

Apply product rule: Apply the power of a product rule, which states that $(ab)^n = a^n \times b^n$ , to the expression $(x^{-3}y^{3})^{-7}$ . $\newline$ $(x^{-3}y^{3})^{-7} = x^{-3 \times -7} \times y^{3 \times -7}$
Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. $\newline$ $x^{(-3 \cdot -7)} \cdot y^{(3 \cdot -7)} = x^{21} \cdot y^{-21}$
Check answer choices: Check the answer choices to see which one matches the simplified expression. $\newline$ The expression $x^{21} \cdot y^{-21}$ matches answer choice (A).