Algebra Examples

${(\frac{x^{3} y}{y^{7} z^{2}})}^{2}$

Step 1

Cancel the common factor of $y$ and $y^{7}$ .

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Step 1.1

Factor $y$ out of $x^{3} y$ .

${(\frac{y x^{3}}{y^{7} z^{2}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $y$ out of $y^{7} z^{2}$ .

${(\frac{y x^{3}}{y (y^{6} z^{2})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{y x^{3}}{y (y^{6} z^{2})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{x^{3}}{y^{6} z^{2}})}^{2}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{x^{3}}{y^{6} z^{2}}$ .

$\frac{{(x^{3})}^{2}}{{(y^{6} z^{2})}^{2}}$

Step 2.2

Apply the product rule to $y^{6} z^{2}$ .

$\frac{{(x^{3})}^{2}}{{(y^{6})}^{2} {(z^{2})}^{2}}$

Step 3

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

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Step 3.1

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

$\frac{x^{3 \cdot 2}}{{(y^{6})}^{2} {(z^{2})}^{2}}$

Step 3.2

Multiply $3$ by $2$ .

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

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(y^{6})}^{2}$ .

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Step 4.1.1

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

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

Step 4.1.2

Multiply $6$ by $2$ .

$\frac{x^{6}}{y^{12} {(z^{2})}^{2}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{x^{6}}{y^{12} z^{2 \cdot 2}}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{x^{6}}{y^{12} z^{4}}$