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Popular >

simplify (81^{1/2})^5

Solution

simplify

(8 1^{\frac{1}{2}})^{5}

Solution

59049

Solution steps

(8 1^{\frac{1}{2}})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 8 1^{\frac{1}{2} \cdot 5}

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

= 8 1^{\frac{5}{2}}

Factor the number:

81 = 9^{2}

= (9^{2})^{\frac{5}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 9^{2 \cdot \frac{5}{2}}

2 \cdot \frac{5}{2} = 5

= 9^{5}

9^{5} = 59049

= 59049

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Frequently Asked Questions (FAQ)

What is (81^{1/2})^5 ?
The solution to (81^{1/2})^5 is 59049