Algebra Examples

${(2 p q^{2})}^{2} {(p q^{2})}^{4}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $2 p q^{2}$ .

${(2 p)}^{2} {(q^{2})}^{2} {(p q^{2})}^{4}$

Step 1.2

Apply the product rule to $2 p$ .

$2^{2} p^{2} {(q^{2})}^{2} {(p q^{2})}^{4}$

Step 2

Raise $2$ to the power of $2$ .

$4 p^{2} {(q^{2})}^{2} {(p q^{2})}^{4}$

Step 3

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

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Step 3.1

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

$4 p^{2} q^{2 \cdot 2} {(p q^{2})}^{4}$

Step 3.2

Multiply $2$ by $2$ .

$4 p^{2} q^{4} {(p q^{2})}^{4}$

Step 4

Apply the product rule to $p q^{2}$ .

$4 p^{2} q^{4} (p^{4} {(q^{2})}^{4})$

Step 5

Multiply $p^{2}$ by $p^{4}$ by adding the exponents.

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Step 5.1

Move $p^{4}$ .

$4 (p^{4} p^{2}) q^{4} {(q^{2})}^{4}$

Step 5.2

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

$4 p^{4 + 2} q^{4} {(q^{2})}^{4}$

Step 5.3

Add $4$ and $2$ .

$4 p^{6} q^{4} {(q^{2})}^{4}$

Step 6

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

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Step 6.1

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

$4 p^{6} q^{4} q^{2 \cdot 4}$

Step 6.2

Multiply $2$ by $4$ .

$4 p^{6} q^{4} q^{8}$

Step 7

Multiply $q^{4}$ by $q^{8}$ by adding the exponents.

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Step 7.1

Move $q^{8}$ .

$4 p^{6} (q^{8} q^{4})$

Step 7.2

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

$4 p^{6} q^{8 + 4}$

Step 7.3

Add $8$ and $4$ .

$4 p^{6} q^{12}$