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Popular >

simplify \sqrt[20]{16^3}

Solution

simplify

Solution

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

+1

Decimal Notation

1.51571 \dots

Solution steps

Apply radical rule:

= (1 6^{3})^{\frac{1}{20}}

Apply exponent rule:

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

= 1 6^{3 \cdot \frac{1}{20}}

3 \cdot \frac{1}{20} = \frac{3}{20}

= 1 6^{\frac{3}{20}}

Factor the number:

16 = 2^{4}

= (2^{4})^{\frac{3}{20}}

Apply exponent rule:

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

(2^{4})^{\frac{3}{20}} = 2^{4 \cdot \frac{3}{20}} = 2^{\frac{3}{5}}

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

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Frequently Asked Questions (FAQ)

What is \sqrt[20]{16^3} ?
The solution to \sqrt[20]{16^3} is 2^{3/5}