Solve (\frac{2x^5}{(x^2)(x^3)} = \frac{a}{x^2} \frac{

Evaluate

\frac{2 x ^{5}}{x ^{2} \times x ^{3}} = \frac{a}{x ^{2}} \times \frac{b}{x ^{3}}

Reduce the fraction

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2 = \frac{a}{x ^{2}} \times \frac{b}{x ^{3}}

Multiply the terms

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2 = \frac{ab}{x ^{5}}

Swap the sides of the equation

\frac{ab}{x ^{5}} = 2

Cross multiply

ab = x^{5} \times 2

Simplify the equation

ab = 2 x^{5}

Swap the sides of the equation

2 x^{5} = ab

Divide both sides

\frac{2 x ^{5}}{2} = \frac{ab}{2}

Divide the numbers

x^{5} = \frac{ab}{2}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{ab}{2}

Calculate

x = 5 \frac{ab}{2}

Simplify the root

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x = \frac{5 2 ^{4} ab}{2}

Solution

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x = \frac{5 16 ab}{2}

Solve the equation