Algebra Examples

$\frac{{(2 x^{2} y z^{3})}^{2}}{10}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{{(2 x^{2} y)}^{2} {(z^{3})}^{2}}{10}$

Step 1.2

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

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Step 1.2.1

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

$\frac{{(2 x^{2})}^{2} y^{2} {(z^{3})}^{2}}{10}$

Step 1.2.2

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

$\frac{2^{2} {(x^{2})}^{2} y^{2} {(z^{3})}^{2}}{10}$

Step 1.3

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

$\frac{4 {(x^{2})}^{2} y^{2} {(z^{3})}^{2}}{10}$

Step 1.4

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

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Step 1.4.1

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

$\frac{4 x^{2 \cdot 2} y^{2} {(z^{3})}^{2}}{10}$

Step 1.4.2

Multiply $2$ by $2$ .

$\frac{4 x^{4} y^{2} {(z^{3})}^{2}}{10}$

Step 1.5

Multiply the exponents in ${(z^{3})}^{2}$ .

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Step 1.5.1

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

$\frac{4 x^{4} y^{2} z^{3 \cdot 2}}{10}$

Step 1.5.2

Multiply $3$ by $2$ .

$\frac{4 x^{4} y^{2} z^{6}}{10}$

Step 2

Cancel the common factor of $4$ and $10$ .

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Step 2.1

Factor $2$ out of $4 x^{4} y^{2} z^{6}$ .

$\frac{2 (2 x^{4} y^{2} z^{6})}{10}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $10$ .

$\frac{2 (2 x^{4} y^{2} z^{6})}{2 (5)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (2 x^{4} y^{2} z^{6})}{2 \cdot 5}$

Step 2.2.3

Rewrite the expression.

$\frac{2 x^{4} y^{2} z^{6}}{5}$