If 11^(a)=root(6)(11^(5)), what is the value of a ?

Given Equation: We are given the equation 11^(a) = root(6)(11^(5)). To solve for a, we need to express both sides of the equation with the same base and exponent format.Express with Same Base: The sixth root of a number is the same as raising that number to the power of 1/6. Therefore, 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 to 11^(5/6).Equate Exponents: Now we have 11^(a) = 11^(5/6). Since the bases are the same, we can equate the exponents: a = 5/6.Final Answer: We have found the value of a to be 5/6, which is the final answer.

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If
11^(a)=root(6)(11^(5)), what is the value of
a ?

If $11^{a}=\sqrt[6]{11^{5}}$ , what is the value of $a$ ?

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Math Problems

Grade 8

Solve equations using cube roots

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Q. If

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

, what is the value of

a

Given Equation: We are given the equation $11^{a} = \sqrt[6]{11^{5}}$ . To solve for $a$ , we need to express both sides of the equation with the same base and exponent format.
Express with Same Base: The sixth root of a number is the same as raising that number to the power of $\frac{1}{6}$ . Therefore, we can rewrite the equation as $11^{a} = (11^{5})^{\frac{1}{6}}$ .
Simplify Right Side: Using the property of exponents that $(x^{m})^{n} = x^{m*n}$ , we can simplify the right side of the equation to $11^{\frac{5}{6}}$ .
Equate Exponents: Now we have $11^{a} = 11^{\frac{5}{6}}$ . Since the bases are the same, we can equate the exponents: $\newline$ $a = \frac{5}{6}$
Final Answer: We have found the value of $a$ to be $\frac{5}{6}$ , which is the final answer.