What is (sqrt(27))^3 ?

The solution to (sqrt(27))^3 is 81sqrt(3)

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simplify (sqrt(27))^3

simplify

(27)^{3}

813

Decimal Notation

140.29611 \dots

Solution steps

(27)^{3}

Apply exponent rule:

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

(27)^{2 + 1} = (27)^{2} 27

= (27)^{2} 27

Apply exponent rule:

(27)^{2} = 27

= 2727

Prime factorization of

27 : 3^{3}

= 27 3^{3}

Apply exponent rule:

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

3^{3} = 3^{2} \cdot 3

= 27 3^{2} \cdot 3

Apply radical rule:

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

3^{2} \cdot 3 = 3^{2} 3

= 27 3^{2} 3

Apply radical rule:

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

3^{2} = 3

= 27 \cdot 33

Multiply the numbers:

27 \cdot 3 = 81

= 813

((2^{2})^{3})^{2}

3.7 \cdot 1 0^{- 3}