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x^((5)/(6))=32

$x^{\frac{5}{6}}=32$

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Operations with rational exponents

Full solution

Q.

x^{\frac{5}{6}}=32

Recognize Problem: Recognize that we need to find the sixth root of $32$ and then raise it to the fifth power. $\newline$ Calculate the sixth root of $32$ : $32^{1/6}$ . $\newline$ $32$ is $2$ raised to the power of $5$ : $2^5$ . $\newline$ So, $32^{1/6} = (2^5)^{1/6}$ .
Calculate Sixth Root: Simplify the exponent by multiplying $5$ by $1/6$ . $\$(2^5)^{1/6} = 2^{5\cdot1/6}$ \). $\$2^{5/6} = 2^{5/6}$ \).
Simplify Exponent: Realize that we already have $x^{5/6} = 2^{5/6}$ . So, $x$ must be equal to $2$ .

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