Pre-Algebra Examples

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

Step 1

Move ${(x y)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x y^{3})}^{3} {(x y)}^{2}$

Step 2

Apply the product rule to $x y^{3}$ .

$x^{3} {(y^{3})}^{3} {(x y)}^{2}$

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $3$ .

$x^{3} y^{9} {(x y)}^{2}$

Step 4

Apply the product rule to $x y$ .

$x^{3} y^{9} (x^{2} y^{2})$

Step 5

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

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Step 5.1

Move $x^{2}$ .

$x^{2} x^{3} y^{9} y^{2}$

Step 5.2

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

$x^{2 + 3} y^{9} y^{2}$

Step 5.3

Add $2$ and $3$ .

$x^{5} y^{9} y^{2}$

Step 6

Multiply $y^{9}$ by $y^{2}$ by adding the exponents.

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Step 6.1

Move $y^{2}$ .

$x^{5} (y^{2} y^{9})$

Step 6.2

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

$x^{5} y^{2 + 9}$

Step 6.3

Add $2$ and $9$ .

$x^{5} y^{11}$