((3^(-6))/(7^(-3)))^(5)=? Choose 1 answer: (A) (7^(15))/(3^(30)) (B) (3^(15))/(7^(30)) (C) (7^(3))/(3^(-30))

Rewrite with Exponent Property: Rewrite the expression using the property of exponents that states (a^(-n)) = 1/(a^n). ((3^(-6))/(7^(-3)))^(5) can be rewritten as ((1/(3^6))/(1/(7^3)))^(5).Simplify by Flipping Fraction: Simplify the expression inside the parentheses by flipping the fraction in the denominator. This gives us ((1/(3^6))*((7^3)/1))^(5).Multiply Fractions: Multiply the fractions inside the parentheses. This simplifies to ((7^3)/(3^6))^(5).Apply Power of a Power Rule: Apply the power of a power rule, which states (a/b)^(n) = a^(n)/b^(n). This gives us (7^(3*5))/(3^(6*5)).Multiply Exponents: Multiply the exponents inside the parentheses. This simplifies to 7^(15)/3^(30).

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((3^(-6))/(7^(-3)))^(5)=?
Choose 1 answer:
(A)
(7^(15))/(3^(30))
(B)
(3^(15))/(7^(30))
(C)
(7^(3))/(3^(-30))

$\left(\frac{3^{-6}}{7^{-3}}\right)^{5}=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{7^{15}}{3^{30}}$ $\newline$ (B) $\frac{3^{15}}{7^{30}}$ $\newline$ (C) $\frac{7^{3}}{3^{-30}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

\left(\frac{3^{-6}}{7^{-3}}\right)^{5}=?

\newline

Choose

1

answer:

\newline

(A)

\frac{7^{15}}{3^{30}}

\newline

(B)

\frac{3^{15}}{7^{30}}

\newline

(C)

\frac{7^{3}}{3^{-30}}

Rewrite with Exponent Property: Rewrite the expression using the property of exponents that states $(a^{-n}) = \frac{1}{(a^n)}$ . $\left(\frac{3^{-6}}{7^{-3}}\right)^{5}$ can be rewritten as $\left(\frac{1}{3^6}/\frac{1}{7^3}\right)^{5}$ .
Simplify by Flipping Fraction: Simplify the expression inside the parentheses by flipping the fraction in the denominator. $\newline$ This gives us $\left(\frac{1}{3^6}\cdot\frac{7^3}{1}\right)^5$ .
Multiply Fractions: Multiply the fractions inside the parentheses. $\newline$ This simplifies to $\left(\frac{7^3}{3^6}\right)^5$ .
Apply Power of a Power Rule: Apply the power of a power rule, which states $(\frac{a}{b})^{n} = \frac{a^{n}}{b^{n}}$ . $\newline$ This gives us $(\frac{7^{3\times5}}{3^{6\times5}})$ .
Multiply Exponents: Multiply the exponents inside the parentheses. $\newline$ This simplifies to $7^{15}/3^{30}$ .