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Popular >

simplify \sqrt[32]{9^{13}}

Solution

simplify

Solution

3^{\frac{13}{16}}

+1

Decimal Notation

2.44152 \dots

Solution steps

Apply radical rule:

= (9^{13})^{\frac{1}{32}}

Apply exponent rule:

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

= 9^{13 \cdot \frac{1}{32}}

13 \cdot \frac{1}{32} = \frac{13}{32}

= 9^{\frac{13}{32}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{13}{32}}

Apply exponent rule:

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

(3^{2})^{\frac{13}{32}} = 3^{2 \cdot \frac{13}{32}} = 3^{\frac{13}{16}}

= 3^{\frac{13}{16}}

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Frequently Asked Questions (FAQ)

What is \sqrt[32]{9^{13}} ?
The solution to \sqrt[32]{9^{13}} is 3^{13/16}