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Popular >

simplify (sqrt(81))^5

Solution

simplify

(81)^{5}

Solution

59049

Solution steps

(81)^{5}

Apply exponent rule:

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

(81)^{4 + 1} = (81)^{4} 81

= (81)^{4} 81

(81)^{4} = ((81)^{2})^{2}

= ((81)^{2})^{2} 81

Apply exponent rule:

(81)^{2} = 81

= 8 1^{2} 81

Apply radical rule:

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

81 = 8 1^{\frac{1}{2}}

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

Apply exponent rule:

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

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

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

2 + \frac{1}{2} = \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 (sqrt(81))^5 ?
The solution to (sqrt(81))^5 is 59049