Basic Math Examples

${(- 10 n)}^{2} {(- 4 n^{3})}^{3}$

Step 1

Apply the product rule to $- 10 n$ .

${(- 10)}^{2} n^{2} {(- 4 n^{3})}^{3}$

Step 2

Raise $- 10$ to the power of $2$ .

$100 n^{2} {(- 4 n^{3})}^{3}$

Step 3

Apply the product rule to $- 4 n^{3}$ .

$100 n^{2} ({(- 4)}^{3} {(n^{3})}^{3})$

Step 4

Rewrite using the commutative property of multiplication.

$100 \cdot {(- 4)}^{3} n^{2} {(n^{3})}^{3}$

Step 5

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

$100 \cdot - 64 n^{2} {(n^{3})}^{3}$

Step 6

Multiply $100$ by $- 64$ .

$- 6400 n^{2} {(n^{3})}^{3}$

Step 7

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

Tap for more steps...

Step 7.1

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

$- 6400 n^{2} n^{3 \cdot 3}$

Step 7.2

Multiply $3$ by $3$ .

$- 6400 n^{2} n^{9}$

Step 8

Multiply $n^{2}$ by $n^{9}$ by adding the exponents.

Tap for more steps...

Step 8.1

Move $n^{9}$ .

$- 6400 (n^{9} n^{2})$

Step 8.2

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

$- 6400 n^{9 + 2}$

Step 8.3

Add $9$ and $2$ .

$- 6400 n^{11}$