Simplify ((3u^-1)^-1)/(15ub^5)

$\frac{{(3 u^{- 1})}^{- 1}}{15 u b^{5}}$

Step 1

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

$\frac{1}{15 u b^{5} (3 u^{- 1})}$

Step 2

Simplify the denominator.

Multiply $u$ by $u^{- 1}$ by adding the exponents.

Move $u^{- 1}$ .

$\frac{1}{15 (u^{- 1} u) b^{5} \cdot 3}$

Multiply $u^{- 1}$ by $u$ .

Raise $u$ to the power of $1$ .

$\frac{1}{15 (u^{- 1} u^{1}) b^{5} \cdot 3}$

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

$\frac{1}{15 u^{- 1 + 1} b^{5} \cdot 3}$

Add $- 1$ and $1$ .

$\frac{1}{15 u^{0} b^{5} \cdot 3}$

Simplify $15 u^{0} b^{5} \cdot 3$ .

$\frac{1}{15 b^{5} \cdot 3}$

Step 3

Multiply $3$ by $15$ .

$\frac{1}{45 b^{5}}$