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Popular >

simplify sqrt(81^3)

Solution

simplify

8 1^{3}

Solution

729

Solution steps

8 1^{3}

Apply exponent rule:

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

8 1^{2 + 1} = 8 1^{2} \cdot 81

= 8 1^{2} \cdot 81

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

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

= 8 1^{2} 81

Apply radical rule:

a^{2} = a, a \geq 0

8 1^{2} = 81

= 8181

Prime factorization of

81 : 3^{4}

= 81 3^{4}

Apply radical rule:

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