Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $3$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $3$ .

$x^{6} y^{9} {(y^{4})}^{2}$

Step 4

Multiply the exponents in ${(y^{4})}^{2}$ .

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Step 4.1

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

$x^{6} y^{9} y^{4 \cdot 2}$

Step 4.2

Multiply $4$ by $2$ .

$x^{6} y^{9} y^{8}$

Step 5

Multiply $y^{9}$ by $y^{8}$ by adding the exponents.

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Step 5.1

Move $y^{8}$ .

$x^{6} (y^{8} y^{9})$

Step 5.2

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

$x^{6} y^{8 + 9}$

Step 5.3

Add $8$ and $9$ .

$x^{6} y^{17}$