Select the equivalent expression. (a^(-7)*b^(-2))^(-9)=? Choose 1 answer: (A) (a^(63))/(b^(18)) (B) (b^(18))/(a^(63)) (c) a^(63)*b^(18)

Identify base and exponents: Identify the base and the exponents inside the parentheses. In (a^(-7)*b^(-2)), a and b are the bases raised to the exponents -7 and -2, respectively. Base a: Exponent -7 Base b: Exponent -2Apply power of a power rule: Apply the power of a power rule, which states that (x^m)^n = x^(m*n). We will apply this rule to both a^(-7) and b^(-2) with the outer exponent of -9. (a^(-7))^(-9) = a^((-7)*(-9)) b^(-2))^(-9) = b^((-2)*(-9))Perform exponent multiplication: Perform the multiplication of the exponents. a^((-7)*(-9)) = a^(63) b^((-2)*(-9)) = b^(18)Combine results: Combine the results to form the final expression. (a^(-7)*b^(-2))^(-9) = a^(63) * b^(18)Choose equivalent expression: Choose the equivalent expression from the given choices. The correct equivalent expression is a^(63) * b^(18), which matches choice (C).

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(a^{-7}b^{-2})^{-9}=

\newline

Choose

1

answer:

\newline

(A)

\frac{a^{63}}{b^{18}}

\newline

(B)

\frac{b^{18}}{a^{63}}

\newline

(C)

a^{63}b^{18}

Identify base and exponents: Identify the base and the exponents inside the parentheses. In $(a^{(-7)} \cdot b^{(-2)})$ , $a$ and $b$ are the bases raised to the exponents $-7$ and $-2$ , respectively. $\newline$ Base $a$ : Exponent $-7$ $\newline$ Base $b$ : Exponent $-2$
Apply power of a power rule: Apply the power of a power rule, which states that $(x^m)^n = x^{(m*n)}$ . We will apply this rule to both $a^{(-7)}$ and $b^{(-2)}$ with the outer exponent of $-9$ . $\newline$ $(a^{(-7)})^{(-9)} = a^{((-7)*(-9))}$ $\newline$ $(b^{(-2)})^{(-9)} = b^{((-2)*(-9))}$
Perform exponent multiplication: Perform the multiplication of the exponents. $\newline$ $a^{((-7)*(-9))} = a^{63}$ $\newline$ $b^{((-2)*(-9))} = b^{18}$
Combine results: Combine the results to form the final expression. $\newline$ $(a^{-7} \cdot b^{-2})^{-9} = a^{63} \cdot b^{18}$
Choose equivalent expression: Choose the equivalent expression from the given choices. $\newline$ The correct equivalent expression is $a^{63} \cdot b^{18}$ , which matches choice $(C)$ .