11^a=\sqrt[6]{11^5} a=□

Rewrite equation: We are given the equation 11^a = sqrt[6]{11^5}. The sixth root of a number is the same as raising that number to the power of 1/6. So we can rewrite the equation as: 11^a = (11^5)^(1/6)Simplify right side: Using the property of exponents that (x^m)^(n) = x^(m*n), we can simplify the right side of the equation: 11^a = 11^(5*(1/6))Equate exponents: Now we have 11^a = 11^(5/6). Since the bases are the same, we can equate the exponents: a = 5/6

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$11^a = \sqrt[6]{11^5}$ $\newline$ $a = \square$

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Algebra 2

Simplify radical expressions involving fractions

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11^a = \sqrt[6]{11^5}

\newline

a = \square

Rewrite equation: We are given the equation $11^a = \sqrt[6]{11^5}$ . The sixth root of a number is the same as raising that number to the power of $\frac{1}{6}$ . So we can rewrite the equation as: $\newline$ $11^a = (11^5)^{\frac{1}{6}}$
Simplify right side: Using the property of exponents that $(x^m)^n = x^{m*n}$ , we can simplify the right side of the equation: $11^a = 11^{5*(1/6)}$
Equate exponents: Now we have $11^a = 11^{\frac{5}{6}}$ . Since the bases are the same, we can equate the exponents: $\newline$ $a = \frac{5}{6}$