What is 4sqrt(2)*4sqrt(2)*4sqrt(2) ?

The solution to 4sqrt(2)*4sqrt(2)*4sqrt(2) is 128sqrt(2)

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simplify 4sqrt(2)4sqrt(2)4sqrt(2)

simplify

42 \cdot 42 \cdot 42

1282

Decimal Notation

181.01933 \dots

Solution steps

42 \cdot 42 \cdot 42

Apply exponent rule:

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

222 = 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 2^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

= 4 \cdot 4 \cdot 4 \cdot 2^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Apply exponent rule:

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

4 \cdot 4 \cdot 4 = 4^{1 + 1 + 1}

= 4^{1 + 1 + 1} \cdot 2^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Add the numbers:

1 + 1 + 1 = 3

= 4^{3} \cdot 2^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

Combine the fractions

\frac{1}{2} + \frac{1}{2} + \frac{1}{2} : \frac{3}{2}

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

2^{\frac{3}{2}} = 22

= 4^{3} \cdot 22

Factor integer

4 = 2^{2}

= (2^{2})^{3} \cdot 22

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

= 2^{2 \cdot 3} \cdot 22

Refine

= 2^{6} \cdot 22

Apply exponent rule:

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

2^{6} \cdot 2 = 2^{6 + 1}

= 2^{6 + 1} 2

Add the numbers:

6 + 1 = 7

= 2^{7} 2

2^{7} = 128

= 1282

e^{3} \cdot e^{- 3}

[(- 2)^{5}]^{3}

What is 4sqrt(2)*4sqrt(2)*4sqrt(2) ?
The solution to 4sqrt(2)*4sqrt(2)*4sqrt(2) is 128sqrt(2)