Simplify the following expression in terms of fractional exponents.
$$
\sqrt[4]{(9 x)^{5}}
$$

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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To simplify the expression $\sqrt[4]{(9x)^5}$ in terms of fractional exponents, we first rewrite the fourth root as an exponent. ‖ ‖ step 2 ⋮ The fourth root of a number can be written as raising that number to the power of $\frac{1}{4}$. So, $\sqrt[4]{(9x)^5}$ becomes $((9x)^5)^{\frac{1}{4}}$. ‖ ‖ step 3 ⋮ Next, we use the property of exponents that states $(a^m)^n = a^{m \cdot n}$. Applying this property, we get $((9x)^5)^{\frac{1}{4}} = (9x)^{5 \cdot \frac{1}{4}}$. ‖ ‖ step 4 ⋮ Simplify the exponent: $5 \cdot \frac{1}{4} = \frac{5}{4}$. Therefore, $(9x)^{\frac{5}{4}}$. ‖ ∻Answer∻ ⚹ $(9x)^{\frac{5}{4}}$ ⚹ ∻Key Concept∻ ⚹Fractional Exponents⚹ ∻Explanation∻ ⚹Fractional exponents are another way to represent roots. The expression $\sqrt[4]{(9x)^5}$ can be rewritten using the exponent $\frac{1}{4}$, and then simplified using the properties of exponents.⚹◊What is the simplified form of $\sqrt[4]{(9x)^5}$ in terms of fractional exponents⍭ Generate me a similar question◊

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