Write the Fraction in Simplest Form ((3k)^3)/(2k^-10)

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

Step 1

Move $k^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

Apply the product rule to $3 k$ .

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

Multiply $k^{3}$ by $k^{10}$ by adding the exponents.

Move $k^{10}$ .

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

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

$\frac{3^{3} k^{10 + 3}}{2}$

Add $10$ and $3$ .

$\frac{3^{3} k^{13}}{2}$

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

$\frac{27 k^{13}}{2}$