Algebra Examples

${(\frac{3 x^{2}}{2 y^{2}})}^{5}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $\frac{3 x^{2}}{2 y^{2}}$ .

$\frac{{(3 x^{2})}^{5}}{{(2 y^{2})}^{5}}$

Step 1.2

Apply the product rule to $3 x^{2}$ .

$\frac{3^{5} {(x^{2})}^{5}}{{(2 y^{2})}^{5}}$

Step 1.3

Apply the product rule to $2 y^{2}$ .

$\frac{3^{5} {(x^{2})}^{5}}{2^{5} {(y^{2})}^{5}}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $3$ to the power of $5$ .

$\frac{243 {(x^{2})}^{5}}{2^{5} {(y^{2})}^{5}}$

Step 2.2

Multiply the exponents in ${(x^{2})}^{5}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{243 x^{2 \cdot 5}}{2^{5} {(y^{2})}^{5}}$

Step 2.2.2

Multiply $2$ by $5$ .

$\frac{243 x^{10}}{2^{5} {(y^{2})}^{5}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $2$ to the power of $5$ .

$\frac{243 x^{10}}{32 {(y^{2})}^{5}}$

Step 3.2

Multiply the exponents in ${(y^{2})}^{5}$ .

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Step 3.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{243 x^{10}}{32 y^{2 \cdot 5}}$

Step 3.2.2

Multiply $2$ by $5$ .

$\frac{243 x^{10}}{32 y^{10}}$