Simplify (10k^10)/((2k^-2)^-3)

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

Step 1

Move ${(2 k^{- 2})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$10 k^{10} {(2 k^{- 2})}^{3}$

Step 2

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

$10 k^{10} {(2 \frac{1}{k^{2}})}^{3}$

Step 3

Combine $2$ and $\frac{1}{k^{2}}$ .

$10 k^{10} {(\frac{2}{k^{2}})}^{3}$

Step 4

Simplify the expression.

Apply the product rule to $\frac{2}{k^{2}}$ .

$10 k^{10} \frac{2^{3}}{{(k^{2})}^{3}}$

Raise $2$ to the power of $3$ .

$10 k^{10} \frac{8}{{(k^{2})}^{3}}$

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

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

$10 k^{10} \frac{8}{k^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$10 k^{10} \frac{8}{k^{6}}$

Step 5

Cancel the common factor of $k^{6}$ .

Factor $k^{6}$ out of $10 k^{10}$ .

$k^{6} (10 k^{4}) \frac{8}{k^{6}}$

Cancel the common factor.

$k^{6} (10 k^{4}) \frac{8}{k^{6}}$

Rewrite the expression.

$10 k^{4} \cdot 8$

Step 6

Multiply $8$ by $10$ .

$80 k^{4}$