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Popular >

simplify 7^{1/5}*49^{7/5}

Solution

simplify

7^{\frac{1}{5}} \cdot 4 9^{\frac{7}{5}}

Solution

343

Solution steps

7^{\frac{1}{5}} \cdot 4 9^{\frac{7}{5}}

Factor integer

49 = 7^{2}

= 7^{\frac{1}{5}} (7^{2})^{\frac{7}{5}}

Apply exponent rule:

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

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

= 7^{\frac{1}{5}} \cdot 7^{2 \cdot \frac{7}{5}}

Refine

= 7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}

Apply exponent rule:

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

7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}

= 7^{\frac{1}{5} + \frac{14}{5}}

Join

\frac{1}{5} + \frac{14}{5} : 3

= 7^{3}

7^{3} = 343

= 343

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Frequently Asked Questions (FAQ)

What is 7^{1/5}*49^{7/5} ?
The solution to 7^{1/5}*49^{7/5} is 343