Basic Math Examples

${(4 p^{2})}^{3} p^{- 15}$

Step 1

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

$4^{3} {(p^{2})}^{3} p^{- 15}$

Step 2

Raise $4$ to the power of $3$ .

$64 {(p^{2})}^{3} p^{- 15}$

Step 3

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

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Step 3.1

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

$64 p^{2 \cdot 3} p^{- 15}$

Step 3.2

Multiply $2$ by $3$ .

$64 p^{6} p^{- 15}$

Step 4

Multiply $p^{6}$ by $p^{- 15}$ by adding the exponents.

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Step 4.1

Move $p^{- 15}$ .

$64 (p^{- 15} p^{6})$

Step 4.2

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

$64 p^{- 15 + 6}$

Step 4.3

Add $- 15$ and $6$ .

$64 p^{- 9}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$64 \frac{1}{p^{9}}$

Step 6

Combine $64$ and $\frac{1}{p^{9}}$ .

$\frac{64}{p^{9}}$