Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $x^{- 2}$ .

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

Step 2.2

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

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

Step 2.3

Add $- 2$ and $3$ .

$x^{1} {(y^{2})}^{3}$

Step 3

Simplify $x^{1} {(y^{2})}^{3}$ .

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

Step 4

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 4.1

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

$x y^{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$x y^{6}$