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Popular >

simplify 9^{3/7}*3^{1/7}

Solution

simplify

9^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

Solution

3

Solution steps

9^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

Factor integer

9 = 3^{2}

= (3^{2})^{\frac{3}{7}} \cdot 3^{\frac{1}{7}}

Apply exponent rule:

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

(3^{2})^{\frac{3}{7}} = 3^{2 \cdot \frac{3}{7}}

= 3^{2 \cdot \frac{3}{7}} \cdot 3^{\frac{1}{7}}

Refine

= 3^{\frac{6}{7}} \cdot 3^{\frac{1}{7}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{\frac{6}{7}} \cdot 3^{\frac{1}{7}} = 3^{\frac{6}{7} + \frac{1}{7}}

= 3^{\frac{6}{7} + \frac{1}{7}}

Join

\frac{6}{7} + \frac{1}{7} : 1

= 3^{1}

Apply rule

a^{1} = a

= 3

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Frequently Asked Questions (FAQ)

What is 9^{3/7}*3^{1/7} ?
The solution to 9^{3/7}*3^{1/7} is 3