Algebra Examples

${(x^{2} y^{6} \cdot x y^{- 4})}^{3}$

Step 1

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

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Step 1.1

Move $x$ .

${(x \cdot x^{2} y^{6} \cdot y^{- 4})}^{3}$

Step 1.2

Multiply $x$ by $x^{2}$ .

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Step 1.2.1

Raise $x$ to the power of $1$ .

${(x^{1} x^{2} y^{6} \cdot y^{- 4})}^{3}$

Step 1.2.2

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

${(x^{1 + 2} y^{6} \cdot y^{- 4})}^{3}$

Step 1.3

Add $1$ and $2$ .

${(x^{3} y^{6} \cdot y^{- 4})}^{3}$

Step 2

Multiply $y^{6}$ by $y^{- 4}$ by adding the exponents.

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Step 2.1

Move $y^{- 4}$ .

${(x^{3} (y^{- 4} y^{6}))}^{3}$

Step 2.2

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

${(x^{3} y^{- 4 + 6})}^{3}$

Step 2.3

Add $- 4$ and $6$ .

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

Step 3

Apply the product rule to $x^{3} y^{2}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $3$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $2$ by $3$ .

$x^{9} y^{6}$