Select the equivalent expression. ((a^(-3))/(b^(2)))^(4)=? Choose 1 answer: (A) (b^(2))/(a^(7)) (B) (1)/(a^(12)*b^(8)) (c) ((b)/(a))^(20)

Identify base and exponents: Identify the base and the exponents in the given expression. In ((a^(-3))/(b^(2)))^(4), the base of the numerator is a with an exponent of -3, and the base of the denominator is b with an exponent of 2. The entire fraction is raised to the power of 4.Apply power of a power rule: Apply the power of a power rule, which states that (x^(m))^n = x^(m*n). In this case, we apply the rule to both the numerator and the denominator separately. ((a^(-3))^4)/((b^(2))^4) = a^(-3*4)/b^(2*4)Perform exponent multiplication: Perform the multiplication of the exponents. a^(-3*4) = a^(-12) b^(2*4) = b^(8) So, the expression becomes a^(-12)/b^(8).Recognize negative exponent: Recognize that a^(-12) is the same as 1/(a^(12)) and rewrite the expression accordingly. (1/(a^(12)))/(b^(8)) = 1/(a^(12)*b^(8))Choose equivalent expression: Choose the equivalent expression for ((a^(-3))/(b^(2)))^(4). The equivalent expression is 1/(a^(12)*b^(8)).

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Select the equivalent expression.

((a^(-3))/(b^(2)))^(4)=?
Choose 1 answer:
(A)
(b^(2))/(a^(7))
(B)
(1)/(a^(12)*b^(8))
(c)
((b)/(a))^(20)

Select the equivalent expression. $\newline$ $\left(\frac{a^{-3}}{b^{2}}\right)^{4}=\,?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{b^{2}}{a^{7}}$ $\newline$ (B) $\frac{1}{a^{12}b^{8}}$ $\newline$ (C) $\left(\frac{b}{a}\right)^{20}$

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{a^{-3}}{b^{2}}\right)^{4}=\,?

\newline

Choose

1

answer:

\newline

(A)

\frac{b^{2}}{a^{7}}

\newline

(B)

\frac{1}{a^{12}b^{8}}

\newline

(C)

\left(\frac{b}{a}\right)^{20}

Identify base and exponents: Identify the base and the exponents in the given expression. In $\left(\frac{a^{-3}}{b^{2}}\right)^{4}$ , the base of the numerator is $a$ with an exponent of $-3$ , and the base of the denominator is $b$ with an exponent of $2$ . The entire fraction is raised to the power of $4$ .
Apply power of a power rule: Apply the power of a power rule, which states that $(x^{m})^{n} = x^{m \cdot n}$ . In this case, we apply the rule to both the numerator and the denominator separately. $\newline$ $\left(a^{-3}\right)^{4}/\left(b^{2}\right)^{4} = a^{-3 \cdot 4}/b^{2 \cdot 4}$
Perform exponent multiplication: Perform the multiplication of the exponents. $\newline$ $a^{(-3 \cdot 4)} = a^{-12}$ $\newline$ $b^{(2 \cdot 4)} = b^{8}$ $\newline$ So, the expression becomes $\frac{a^{-12}}{b^{8}}$ .
Recognize negative exponent: Recognize that $a^{-12}$ is the same as $\frac{1}{a^{12}}$ and rewrite the expression accordingly. $\newline$ $\frac{1}{a^{12}}\bigg/\frac{1}{b^{8}} = \frac{1}{a^{12} \cdot b^{8}}$
Choose equivalent expression: Choose the equivalent expression for $\left(\frac{a^{-3}}{b^{2}}\right)^{4}$ . $\newline$ The equivalent expression is $\frac{1}{a^{12}b^{8}}$ .