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Popular >

simplify sqrt(81)^3

Solution

simplify

81^{3}

Solution

729

Solution steps

(81)^{3}

Apply exponent rule:

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

(81)^{2 + 1} = (81)^{2} 81

= (81)^{2} 81

Apply exponent rule:

(n a)^{n} = a, n i s o dd or a \geq 0

(81)^{2} = 81

= 8181

Prime factorization of

81 : 3^{4}

= 81 3^{4}

Apply radical rule:

n a^{m} = a^{\frac{m}{n}}, a \geq 0

3^{4} = 3^{\frac{4}{2}}

= 81 \cdot 3^{\frac{4}{2}}

Divide the numbers:

\frac{4}{2} = 2

= 81 \cdot 3^{2}

3^{2} = 9

= 81 \cdot 9

Multiply the numbers:

81 \cdot 9 = 729

= 729

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Frequently Asked Questions (FAQ)

What is sqrt(81)^3 ?
The solution to sqrt(81)^3 is 729