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Popular >

simplify 3^{2/3}*9^{2/3}

Solution

simplify

3^{\frac{2}{3}} \cdot 9^{\frac{2}{3}}

Solution

9

Solution steps

3^{\frac{2}{3}} \cdot 9^{\frac{2}{3}}

Apply exponent rule:

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

3^{\frac{2}{3}} \cdot 9^{\frac{2}{3}} = (3 \cdot 9)^{\frac{2}{3}}

= (3 \cdot 9)^{\frac{2}{3}}

Multiply the numbers:

3 \cdot 9 = 27

= 2 7^{\frac{2}{3}}

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

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

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

= 3^{2}

Refine

= 9

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Frequently Asked Questions (FAQ)

What is 3^{2/3}*9^{2/3} ?
The solution to 3^{2/3}*9^{2/3} is 9