Algebra Examples

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

Step 1

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Add $2$ and $5$ .

$\frac{4 y^{2} \cdot {(x^{2})}^{5}}{x^{7}}$

Step 2

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

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Step 2.1

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

$\frac{4 y^{2} x^{2 \cdot 5}}{x^{7}}$

Step 2.2

Multiply $2$ by $5$ .

$\frac{4 y^{2} x^{10}}{x^{7}}$

Step 3

Cancel the common factor of $x^{10}$ and $x^{7}$ .

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Step 3.1

Factor $x^{7}$ out of $4 y^{2} x^{10}$ .

$\frac{x^{7} (4 y^{2} x^{3})}{x^{7}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{x^{7} (4 y^{2} x^{3})}{x^{7} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{7} (4 y^{2} x^{3})}{x^{7} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{4 y^{2} x^{3}}{1}$

Step 3.2.4

Divide $4 y^{2} x^{3}$ by $1$ .

$4 y^{2} x^{3}$