Basic Math Examples

${(- 4 p^{4} q^{7})}^{6}$

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 $- 4 p^{4} q^{7}$ .

${(- 4 p^{4})}^{6} {(q^{7})}^{6}$

Step 1.2

Apply the product rule to $- 4 p^{4}$ .

${(- 4)}^{6} {(p^{4})}^{6} {(q^{7})}^{6}$

Step 2

Raise $- 4$ to the power of $6$ .

$4096 {(p^{4})}^{6} {(q^{7})}^{6}$

Step 3

Multiply the exponents in ${(p^{4})}^{6}$ .

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Step 3.1

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

$4096 p^{4 \cdot 6} {(q^{7})}^{6}$

Step 3.2

Multiply $4$ by $6$ .

$4096 p^{24} {(q^{7})}^{6}$

Step 4

Multiply the exponents in ${(q^{7})}^{6}$ .

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Step 4.1

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

$4096 p^{24} q^{7 \cdot 6}$

Step 4.2

Multiply $7$ by $6$ .

$4096 p^{24} q^{42}$