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

Question

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. The fourth root of a number is the same as raising that number to the power of $\frac{1}{4}$. ‖ ‖ step 2 ⋮ Therefore, $\sqrt[4]{(9x)^{5}}$ can be rewritten as $((9x)^{5})^{\frac{1}{4}}$. ‖ ‖ 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 ⋮ Simplifying the exponent, we have $(9x)^{\frac{5}{4}}$. ‖ ∻Answer∻ ⚹ $(9x)^{\frac{5}{4}}$ ⚹ ∻Key Concept∻ ⚹Fractional Exponents⚹ ∻Explanation∻ ⚹The fourth root of a number can be expressed as raising that number to the power of $\frac{1}{4}$. Using the properties of exponents, we can simplify the given expression in terms of fractional exponents.⚹◊What is the simplified expression in terms of fractional exponents for $\sqrt[4]{(9x)^{5}}$?⍭ Generate me a similar question◊

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