Simplify the expression to a single power of $x$ .
${(\frac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}})}^{\frac{2}{3}}$

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Answer

The simplified expression is $x^{\frac{5}{18}}$

Steps

Step 1 ：Apply the property of exponents: ${(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}}$

Step 2 ：Apply the property to the given expression: ${(\frac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}})}^{\frac{2}{3}} = \frac{(x^{\frac{3}{4}})^{\frac{2}{3}}}{(x^{\frac{1}{3}})^{\frac{2}{3}}}$

Step 3 ：Simplify the exponents by multiplying the numerator and denominator by the exponent: $\frac{x^{\frac{3}{4} \cdot \frac{2}{3}}}{x^{\frac{1}{3} \cdot \frac{2}{3}}} = \frac{x^{\frac{1}{2}}}{x^{\frac{2}{9}}}$

Step 4 ：Divide the exponents by subtracting them: $x^{\frac{1}{2} - \frac{2}{9}} = x^{\frac{9}{18} - \frac{4}{18}} = x^{\frac{5}{18}}$

Step 5 ：The simplified expression is $x^{\frac{5}{18}}$

Simplify the expression to a single power of x.(x34x13)23

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Popular Problems

Simplify the expression to a single power of $x$ .
${(\frac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}})}^{\frac{2}{3}}$