What is ((sqrt(2))/2)^3 ?

The solution to ((sqrt(2))/2)^3 is 1/(2sqrt(2))

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simplify ((sqrt(2))/2)^3

simplify

(\frac{2}{2})^{3}

\frac{1}{2 2}

Decimal Notation

0.35355 \dots

Solution steps

(\frac{2}{2})^{3}

Apply exponent rule:

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

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

2^{3} = 8

= \frac{( 2 ) ^{3}}{8}

(2)^{3} = 22

= \frac{2 2}{8}

Cancel the common factor:

2

= \frac{2}{4}

Factor

4 : 2^{2}

= \frac{2}{2 ^{2}}

Cancel

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

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

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

= \frac{1}{2 2}

5 x^{2} + 3 x + 2 = 0

24 x - 56 y + 72

15 (x - 3) - 14 x \geq 14

\frac{1}{3} (6 x - 3) = 11

1 - y^{12}