Which expression is equivalent to (11^1)^6? Choices: (A)11^7 (B)1/11^7 (C)11^6 (D)1/11^6

Apply power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). So, (11^1)^6 = 11^(1*6) = 11^6.Compare with choices: Compare the result with the given choices. We have found that (11^1)^6 = 11^6. Now, we look at the choices to find the equivalent expression. (A) 11^7 is not correct because 7 is not the product of 1 and 6. (B) 1/11^7 is not correct because it represents the reciprocal of 11^7, not 11^6. (C) 11^6 is correct because it matches our calculation. (D) 1/11^6 is not correct because it represents the reciprocal of 11^6, not 11^6 itself.

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(11^1)^6

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Choices:

\newline

(A)

11^7

\newline

(B)

\frac{1}{11^7}

\newline

(C)

11^6

\newline

(D)

\frac{1}{11^6}

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . $\newline$ So, $(11^1)^6 = 11^{1*6} = 11^6$ .
Compare with choices: Compare the result with the given choices. $\newline$ We have found that 11^1)^6 = 11^6\.$\newlineNow, we look at the choices to find the equivalent expression. $\newline$ (A) \$11^7$ is not correct because $7$ is not the product of $1$ and $6$.$\newline$(B) $rac{1}{11^7}$ is not correct because it represents the reciprocal of $11^7$, not $11^6$.$\newline$(C) $11^6$ is correct because it matches our calculation.$\newline$(D) $rac{1}{11^6}$ is not correct because it represents the reciprocal of $11^6$, not $11^6$ itself.