What is (3^{2/3}*5^{1/4})^6 ?

The solution to (3^{2/3}*5^{1/4})^6 is 405*5^{1/2}

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simplify (3^{2/3}*5^{1/4})^6

simplify

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6}

405 \cdot 5^{\frac{1}{2}}

Decimal Notation

905.60753 \dots

Solution steps

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6} = (3^{\frac{2}{3}})^{6} (5^{\frac{1}{4}})^{6}

= (3^{\frac{2}{3}})^{6} (5^{\frac{1}{4}})^{6}

(3^{\frac{2}{3}})^{6} = 81

= 81 (5^{\frac{1}{4}})^{6}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{\frac{1}{4}})^{6} = 5^{\frac{1}{4} \cdot 6}

= 81 \cdot 5^{\frac{1}{4} \cdot 6}

\frac{1}{4} \cdot 6 = \frac{3}{2}

= 81 \cdot 5^{\frac{3}{2}}

5^{\frac{3}{2}} = 5 \cdot 5^{\frac{1}{2}}

= 81 \cdot 5 \cdot 5^{\frac{1}{2}}

Multiply the numbers:

81 \cdot 5 = 405

= 405 \cdot 5^{\frac{1}{2}}

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What is (3^{2/3}*5^{1/4})^6 ?
The solution to (3^{2/3}*5^{1/4})^6 is 405*5^{1/2}