If 11^(a)=root(4)(11^(3)), what is the value of a ?

Rewrite with Same Base: We are given the equation 11^(a) = root(4)(11^(3)). To solve for a, we need to express both sides of the equation with the same base and exponent format.Apply Fourth Root Property: The fourth root of a number is the same as raising that number to the power of 1/4. Therefore, we can rewrite the equation as 11^(a) = (11^(3))^(1/4).Simplify Exponents: Using the property of exponents that (x^(m))^(n) = x^(m*n), we can simplify the right side of the equation to 11^(3/4). 11^(a) = 11^(3/4)Set Exponents Equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. This gives us a = 3/4.

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If
11^(a)=root(4)(11^(3)), what is the value of
a ?

If $11^{a}=\sqrt[4]{11^{3}}$ , 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[4]{11^{3}}

, what is the value of

a

Given Equation: We are given the equation $11^{a} = \sqrt[4]{11^{3}}$ . 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 fourth root of a number is the same as raising that number to the power of $\frac{1}{4}$ . Therefore, we can rewrite the equation as $11^{a} = (11^{3})^{\frac{1}{4}}$ .
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 $11^{\frac{3}{4}}$ .
Equate Exponents: Now we have $11^{a} = 11^{\frac{3}{4}}$ . Since the bases are the same, we can equate the exponents: $\newline$ $a = \frac{3}{4}$
Final Answer: We have found the value of $a$ to be $\frac{3}{4}$ , which is the final answer.