Precalculus Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $3$ .

$x^{6} y^{3} {(x y^{3})}^{2}$

Step 3

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

$x^{6} y^{3} (x^{2} {(y^{3})}^{2})$

Step 4

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 4.1

Move $x^{2}$ .

$x^{2} x^{6} y^{3} {(y^{3})}^{2}$

Step 4.2

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

$x^{2 + 6} y^{3} {(y^{3})}^{2}$

Step 4.3

Add $2$ and $6$ .

$x^{8} y^{3} {(y^{3})}^{2}$

Step 5

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

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Step 5.1

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

$x^{8} y^{3} y^{3 \cdot 2}$

Step 5.2

Multiply $3$ by $2$ .

$x^{8} y^{3} y^{6}$

Step 6

Multiply $y^{3}$ by $y^{6}$ by adding the exponents.

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Step 6.1

Move $y^{6}$ .

$x^{8} (y^{6} y^{3})$

Step 6.2

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

$x^{8} y^{6 + 3}$

Step 6.3

Add $6$ and $3$ .

$x^{8} y^{9}$