Algebra Examples

$x^{2} y^{- 4} \cdot (x^{3} y^{2})$

Step 1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 1.1

Move $x^{3}$ .

$x^{3} x^{2} y^{- 4} \cdot y^{2}$

Step 1.2

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

$x^{3 + 2} y^{- 4} \cdot y^{2}$

Step 1.3

Add $3$ and $2$ .

$x^{5} y^{- 4} \cdot y^{2}$

Step 2

Multiply $y^{- 4}$ by $y^{2}$ by adding the exponents.

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Step 2.1

Move $y^{2}$ .

$x^{5} (y^{2} y^{- 4})$

Step 2.2

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

$x^{5} y^{2 - 4}$

Step 2.3

Subtract $4$ from $2$ .

$x^{5} y^{- 2}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x^{5} \frac{1}{y^{2}}$

Step 4

Combine $x^{5}$ and $\frac{1}{y^{2}}$ .

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