Write the Fraction in Simplest Form (3(k^5)^2)/(-4k^-4)

$\frac{3 {(k^{5})}^{2}}{- 4 k^{- 4}}$

Step 1

Move $k^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 {(k^{5})}^{2} k^{4}}{- 4}$

Step 2

Simplify the numerator.

Multiply the exponents in ${(k^{5})}^{2}$ .

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

$\frac{3 k^{5 \cdot 2} k^{4}}{- 4}$

Multiply $5$ by $2$ .

$\frac{3 k^{10} k^{4}}{- 4}$

Multiply $k^{10}$ by $k^{4}$ by adding the exponents.

Move $k^{4}$ .

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

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

$\frac{3 k^{4 + 10}}{- 4}$

Add $4$ and $10$ .

$\frac{3 k^{14}}{- 4}$

Step 3

Move the negative in front of the fraction.

$- \frac{3 k^{14}}{4}$