Which expression is equivalent to (6^(-1))^(5)×6^(3) ? 36 1 (1)/(36) (1)/(6)

Apply Power Rule: Apply the power of a power rule to (6^(-1))^5. According to the power of a power rule, (a^m)^n = a^(m*n). So, (6^(-1))^5 = 6^(-1*5) = 6^(-5).Combine Exponents: Combine the exponents of the same base using the multiplication property of exponents. We have 6^(-5) * 6^3. According to the multiplication property of exponents, a^m * a^n = a^(m+n) when the bases are the same. So, 6^(-5) * 6^3 = 6^(-5+3) = 6^(-2).Simplify Expression: Simplify the expression 6^(-2). The negative exponent rule states that a^(-n) = 1/(a^n). So, 6^(-2) = 1/(6^2) = 1/36.

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Which expression is equivalent to
(6^(-1))^(5)×6^(3) ?
36
1

(1)/(36)

(1)/(6)

Which expression is equivalent to $\left(6^{-1}\right)^{5} \times 6^{3}$ ? $\newline$ $36$ $\newline$ $1$ $\newline$ $\frac{1}{36}$ $\newline$ $\frac{1}{6}$

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Algebra 2

Multiplication with rational exponents

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Q. Which expression is equivalent to

\left(6^{-1}\right)^{5} \times 6^{3}

\newline

36

\newline

1

\newline

\frac{1}{36}

\newline

\frac{1}{6}

Apply Power Rule: Apply the power of a power rule to $(6^{-1})^5$ . According to the power of a power rule, $(a^m)^n = a^{m*n}$ . So, $(6^{-1})^5 = 6^{-1*5} = 6^{-5}$ .
Combine Exponents: Combine the exponents of the same base using the multiplication property of exponents. $\newline$ We have $6^{-5} \times 6^3$ . $\newline$ According to the multiplication property of exponents, $a^m \times a^n = a^{m+n}$ when the bases are the same. $\newline$ So, $6^{-5} \times 6^3 = 6^{-5+3} = 6^{-2}$ .
Simplify Expression: Simplify the expression $6^{-2}$ . The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . So, $6^{-2} = \frac{1}{6^2} = \frac{1}{36}$ .