What is 1/(8sqrt(8)) ?

The solution to 1/(8sqrt(8)) is 1/(16sqrt(2))

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simplify 1/(8sqrt(8))

simplify

\frac{1}{8 8}

\frac{1}{16 2}

Solution steps

\frac{1}{8 8}

Prime factorization of

8 : 2^{3}

= \frac{1}{8 2 ^{3}}

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

= \frac{1}{8 2 ^{2} 2}

Apply radical rule:

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

2^{2} = 2

= \frac{1}{8 \cdot 2 2}

Multiply the numbers:

8 \cdot 2 = 16

= \frac{1}{16 2}

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