Algebra Examples

$(x^{3} y^{5}) {(x^{4} y^{2})}^{3}$

Step 1

Apply the product rule to $x^{4} y^{2}$ .

$x^{3} y^{5} ({(x^{4})}^{3} {(y^{2})}^{3})$

Step 2

Multiply the exponents in ${(x^{4})}^{3}$ .

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Step 2.1

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

$x^{3} y^{5} (x^{4 \cdot 3} {(y^{2})}^{3})$

Step 2.2

Multiply $4$ by $3$ .

$x^{3} y^{5} (x^{12} {(y^{2})}^{3})$

Step 3

Multiply $x^{3}$ by $x^{12}$ by adding the exponents.

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Step 3.1

Move $x^{12}$ .

$x^{12} x^{3} y^{5} {(y^{2})}^{3}$

Step 3.2

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

$x^{12 + 3} y^{5} {(y^{2})}^{3}$

Step 3.3

Add $12$ and $3$ .

$x^{15} y^{5} {(y^{2})}^{3}$

Step 4

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

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Step 4.1

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

$x^{15} y^{5} y^{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$x^{15} y^{5} y^{6}$

Step 5

Multiply $y^{5}$ by $y^{6}$ by adding the exponents.

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Step 5.1

Move $y^{6}$ .

$x^{15} (y^{6} y^{5})$

Step 5.2

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

$x^{15} y^{6 + 5}$

Step 5.3

Add $6$ and $5$ .

$x^{15} y^{11}$