What is sqrt(32n)^{3/2} ?

The solution to sqrt(32n)^{3/2} is 8*2^{3/4}n^{3/4}

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simplify sqrt(32n)^{3/2}

simplify

32 n^{\frac{3}{2}}

8 \cdot 2^{\frac{3}{4}} n^{\frac{3}{4}}

Solution steps

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

Simplify

32 n : 42 n

= (42 n)^{\frac{3}{2}}

Apply exponent rule:

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

(42 n)^{\frac{3}{2}} = 4^{\frac{3}{2}} (2)^{\frac{3}{2}} (n)^{\frac{3}{2}}

= 4^{\frac{3}{2}} (2)^{\frac{3}{2}} (n)^{\frac{3}{2}}

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

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

(2)^{\frac{3}{2}} = 2^{\frac{3}{4}}

= 8 \cdot 2^{\frac{3}{4}} (n)^{\frac{3}{2}}

(n)^{\frac{3}{2}} = n^{\frac{3}{4}}

= 8 \cdot 2^{\frac{3}{4}} n^{\frac{3}{4}}

(\frac{1}{3 ( x - 1 ) ^{\frac{2}{3}}})^{2}

2 \cdot 1 0^{4} + 3 \cdot 1 0^{4}

\frac{tan ( x )}{cos ^{2} ( x )}

(2 x + 3)^{2} - (2 x - 3)^{2}