What is (sqrt(2sin(2x)))^3 ?

The solution to (sqrt(2sin(2x)))^3 is 2sqrt(2)sin^{3/2}(2x)

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simplify (sqrt(2sin(2x)))^3

simplify

(2 sin (2 x))^{3}

22 sin^{\frac{3}{2}} (2 x)

Solution steps

(2 sin (2 x))^{3}

Apply radical rule:

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

= ((2 sin (2 x))^{\frac{1}{2}})^{3}

Apply exponent rule:

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

= (2 sin (2 x))^{\frac{1}{2} \cdot 3}

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

= 22 sin^{\frac{3}{2}} (2 x)

a (x + 1)^{2} (x^{2} + 4)^{2}

33.2 \cdot 1 0^{- 2}

0.8 e^{- 3 (0.1)}

π (5.9675 \cdot 1 0^{- 5} m^{2})

2.713 \cdot 1 0^{- 1}

What is (sqrt(2sin(2x)))^3 ?
The solution to (sqrt(2sin(2x)))^3 is 2sqrt(2)sin^{3/2}(2x)