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Popular >

simplify \sqrt[11]{100^{5.5}}

Solution

simplify

Solution

10

Solution steps

Apply radical rule:

= (10 0^{5.5})^{\frac{1}{11}}

Apply exponent rule:

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

= 10 0^{5.5 \cdot \frac{1}{11}}

5.5 \cdot \frac{1}{11} = 0.5

= 10 0^{0.5}

a^{\frac{1}{2}} = a

= 100

Factor the number:

100 = 1 0^{2}

= 1 0^{2}

Apply exponent rule:

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

1 0^{2} = 1 0^{2 \cdot \frac{1}{2}} = 10

= 10

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Frequently Asked Questions (FAQ)

What is \sqrt[11]{100^{5.5}} ?
The solution to \sqrt[11]{100^{5.5}} is 10