Pre-Algebra Examples

$y^{5} \cdot y^{3} \div y^{2}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Multiply $y^{5}$ by $y^{3}$ by adding the exponents.

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Step 2.1

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

$\frac{y^{5 + 3}}{y^{2}}$

Step 2.2

Add $5$ and $3$ .

$\frac{y^{8}}{y^{2}}$

Step 3

Cancel the common factor of $y^{8}$ and $y^{2}$ .

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Step 3.1

Factor $y^{2}$ out of $y^{8}$ .

$\frac{y^{2} y^{6}}{y^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{y^{2} y^{6}}{y^{2} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{2} y^{6}}{y^{2} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{6}}{1}$

Step 3.2.4

Divide $y^{6}$ by $1$ .

$y^{6}$