Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $y$ .

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

Step 2.2

Multiply $y$ by $y^{3}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $1$ and $3$ .

${(x^{2})}^{3} y^{4} x$

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $3$ .

$x^{6} y^{4} x$

Step 4

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$x \cdot x^{6} y^{4}$

Step 4.2

Multiply $x$ by $x^{6}$ .

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Step 4.2.1

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

$x^{1} x^{6} y^{4}$

Step 4.2.2

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

$x^{1 + 6} y^{4}$

Step 4.3

Add $1$ and $6$ .

$x^{7} y^{4}$