Simplify (12d^10)/(3(d^-4)^2)

$\frac{12 d^{10}}{3 {(d^{- 4})}^{2}}$

Step 1

Cancel the common factor of $12$ and $3$ .

Factor $3$ out of $12 d^{10}$ .

$\frac{3 (4 d^{10})}{3 {(d^{- 4})}^{2}}$

Cancel the common factors.

Factor $3$ out of $3 {(d^{- 4})}^{2}$ .

$\frac{3 (4 d^{10})}{3 ({(d^{- 4})}^{2})}$

Cancel the common factor.

$\frac{3 (4 d^{10})}{3 {(d^{- 4})}^{2}}$

Rewrite the expression.

$\frac{4 d^{10}}{{(d^{- 4})}^{2}}$

Step 2

Simplify the denominator.

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

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

$\frac{4 d^{10}}{d^{- 4 \cdot 2}}$

Multiply $- 4$ by $2$ .

$\frac{4 d^{10}}{d^{- 8}}$

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

$\frac{4 d^{10}}{\frac{1}{d^{8}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$4 d^{10} d^{8}$

Step 4

Multiply $d^{10}$ by $d^{8}$ by adding the exponents.

Move $d^{8}$ .

$4 (d^{8} d^{10})$

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

$4 d^{8 + 10}$

Add $8$ and $10$ .

$4 d^{18}$