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Popular >

simplify 9^{2/5}*27^{2/5}

Solution

simplify

9^{\frac{2}{5}} \cdot 2 7^{\frac{2}{5}}

Solution

9

Solution steps

9^{\frac{2}{5}} \cdot 2 7^{\frac{2}{5}}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

9^{\frac{2}{5}} \cdot 2 7^{\frac{2}{5}} = (9 \cdot 27)^{\frac{2}{5}}

= (9 \cdot 27)^{\frac{2}{5}}

Multiply the numbers:

9 \cdot 27 = 243

= 24 3^{\frac{2}{5}}

Factor the number:

243 = 3^{5}

= (3^{5})^{\frac{2}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

= 3^{2}

Refine

= 9

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Frequently Asked Questions (FAQ)

What is 9^{2/5}*27^{2/5} ?
The solution to 9^{2/5}*27^{2/5} is 9