Precalculus Examples

${(5 n^{3})}^{2} \cdot n^{- 6}$

Step 1

Apply the product rule to $5 n^{3}$ .

$5^{2} {(n^{3})}^{2} \cdot n^{- 6}$

Step 2

Raise $5$ to the power of $2$ .

$25 {(n^{3})}^{2} \cdot n^{- 6}$

Step 3

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

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Step 3.1

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

$25 n^{3 \cdot 2} \cdot n^{- 6}$

Step 3.2

Multiply $3$ by $2$ .

$25 n^{6} \cdot n^{- 6}$

Step 4

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

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Step 4.1

Move $n^{- 6}$ .

$25 (n^{- 6} n^{6})$

Step 4.2

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

$25 n^{- 6 + 6}$

Step 4.3

Add $- 6$ and $6$ .

$25 n^{0}$

Step 5

Simplify $25 n^{0}$ .

$25$