Which expression is equivalent to (9^7)^3? Choices: (A)1/9^10 (B)1/9^21 (C)9^10 (D)9^21

Apply Power Rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). We will apply this rule to the expression (9^7)^3. (9^7)^3 = 9^(7*3)Multiply Exponents: Multiply the exponents. Now we multiply the exponents 7 and 3 to find the new exponent for the base 9. 9^(7*3) = 9^21Match with Choices: Match the result with the given choices. We have found that (9^7)^3 = 9^21. Now we look at the choices to find the equivalent expression. The correct choice is (D) 9^21.

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Which expression is equivalent to $(9^7)^3$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{9^{10}}$ $\newline$ (B) $\frac{1}{9^{21}}$ $\newline$ (C) $9^{10}$ $\newline$ (D) $9^{21}$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(9^7)^3

\newline

Choices:

\newline

(A)

\frac{1}{9^{10}}

\newline

(B)

\frac{1}{9^{21}}

\newline

(C)

9^{10}

\newline

(D)

9^{21}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{(m*n)}$ . We will apply this rule to the expression $(9^7)^3$ . $\newline$ $(9^7)^3 = 9^{(7*3)}$
Multiply Exponents: Multiply the exponents. $\newline$ Now we multiply the exponents $7$ and $3$ to find the new exponent for the base $9$ . $\newline$ $9^{(7*3)} = 9^{21}$
Match with Choices: Match the result with the given choices. $\newline$ We have found that $(9^7)^3 = 9^{21}$ . Now we look at the choices to find the equivalent expression. $\newline$ The correct choice is (D) $9^{21}$ .