What is (sqrt(32))^3 ?

The solution to (sqrt(32))^3 is 128sqrt(2)

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simplify (sqrt(32))^3

simplify

(32)^{3}

1282

Decimal Notation

181.01933 \dots

Solution steps

(32)^{3}

Apply exponent rule:

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

(32)^{2 + 1} = (32)^{2} 32

= (32)^{2} 32

Apply exponent rule:

(32)^{2} = 32

= 3232

Prime factorization of

32 : 2^{5}

= 32 2^{5}

Apply exponent rule:

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

2^{5} = 2^{4} \cdot 2

= 32 2^{4} \cdot 2

Apply radical rule:

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

2^{4} \cdot 2 = 2^{4} 2

= 32 2^{4} 2

2^{4} = 4

= 32 \cdot 42

Multiply the numbers:

32 \cdot 4 = 128

= 1282

(4 x^{3}) (3 x^{4})

200 e^{- 1} (5 - e^{- 0.002 (400)})

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

e^{- 4} \cdot 8