Pre-Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

$\frac{x^{2 \cdot 5} y^{5}}{x^{3} y}$

Step 1.2.2

Multiply $2$ by $5$ .

$\frac{x^{10} y^{5}}{x^{3} y}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x^{10}$ and $x^{3}$ .

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Step 2.1.1

Factor $x^{3}$ out of $x^{10} y^{5}$ .

$\frac{x^{3} (x^{7} y^{5})}{x^{3} y}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

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

$\frac{x^{3} (x^{7} y^{5})}{x^{3} (y)}$

Step 2.1.2.2

Cancel the common factor.

$\frac{x^{3} (x^{7} y^{5})}{x^{3} y}$

Step 2.1.2.3

Rewrite the expression.

$\frac{x^{7} y^{5}}{y}$

Step 2.2

Cancel the common factor of $y^{5}$ and $y$ .

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Step 2.2.1

Factor $y$ out of $x^{7} y^{5}$ .

$\frac{y (x^{7} y^{4})}{y}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Raise $y$ to the power of $1$ .

$\frac{y (x^{7} y^{4})}{y^{1}}$

Step 2.2.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (x^{7} y^{4})}{y \cdot 1}$

Step 2.2.2.3

Cancel the common factor.

$\frac{y (x^{7} y^{4})}{y \cdot 1}$

Step 2.2.2.4

Rewrite the expression.

$\frac{x^{7} y^{4}}{1}$

Step 2.2.2.5

Divide $x^{7} y^{4}$ by $1$ .

$x^{7} y^{4}$