What is \sqrt[4]{((3mn)/(2a^3b^2))}^8 ?

The solution to \sqrt[4]{((3mn)/(2a^3b^2))}^8 is (9m^2n^2)/(4a^6b^4)

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simplify \sqrt[4]{((3mn)/(2a^3b^2))}^8

simplify

\frac{9 m ^{2} n ^{2}}{4 a ^{6} b ^{4}}

Solution steps

Apply rule:

(a) = a

(\frac{3 mn}{2 a ^{3} b ^{2}}) = \frac{3 mn}{2 a ^{3} b ^{2}}

Rewrite

8

4 \cdot 2

Apply exponent rule:

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

assuming

a \geq 0

Apply exponent rule:

assuming

n i s o dd or a \geq 0

= (\frac{3 mn}{2 a ^{3} b ^{2}})^{2}

Apply exponent rule:

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

= \frac{( 3 mn ) ^{2}}{( 2 a ^{3} b ^{2} ) ^{2}}

Simplify

(3 mn)^{2} : 9 m^{2} n^{2}

= \frac{9 m ^{2} n ^{2}}{( 2 a ^{3} b ^{2} ) ^{2}}

Simplify

(2 a^{3} b^{2})^{2} : 4 a^{6} b^{4}

= \frac{9 m ^{2} n ^{2}}{4 a ^{6} b ^{4}}

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What is \sqrt[4]{((3mn)/(2a^3b^2))}^8 ?
The solution to \sqrt[4]{((3mn)/(2a^3b^2))}^8 is (9m^2n^2)/(4a^6b^4)