Write the Fraction in Simplest Form (5(u^-3)^2)/(2u^8)

$\frac{5 {(u^{- 3})}^{2}}{2 u^{8}}$

Step 1

Simplify the numerator.

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

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

$\frac{5 u^{- 3 \cdot 2}}{2 u^{8}}$

Multiply $- 3$ by $2$ .

$\frac{5 u^{- 6}}{2 u^{8}}$

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

$\frac{5 \frac{1}{u^{6}}}{2 u^{8}}$

Step 2

Combine $5$ and $\frac{1}{u^{6}}$ .

$\frac{\frac{5}{u^{6}}}{2 u^{8}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{u^{6}} \cdot \frac{1}{2 u^{8}}$

Step 4

Combine.

$\frac{5 \cdot 1}{u^{6} (2 u^{8})}$

Step 5

Multiply $u^{6}$ by $u^{8}$ by adding the exponents.

Move $u^{8}$ .

$\frac{5 \cdot 1}{u^{8} u^{6} \cdot 2}$

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

$\frac{5 \cdot 1}{u^{8 + 6} \cdot 2}$

Add $8$ and $6$ .

$\frac{5 \cdot 1}{u^{14} \cdot 2}$

Step 6

Multiply $5$ by $1$ .

$\frac{5}{u^{14} \cdot 2}$

Step 7

Move $2$ to the left of $u^{14}$ .

$\frac{5}{2 u^{14}}$