Write the Fraction in Simplest Form (2(b^-1j^-2)^-1)/(10b^3)

$\frac{2 {(b^{- 1} j^{- 2})}^{- 1}}{10 b^{3}}$

Step 1

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

$\frac{2}{10 b^{3} (b^{- 1} j^{- 2})}$

Step 2

Multiply $b^{3}$ by $b^{- 1}$ by adding the exponents.

Move $b^{- 1}$ .

$\frac{2}{10 (b^{- 1} b^{3}) j^{- 2}}$

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

$\frac{2}{10 b^{- 1 + 3} j^{- 2}}$

Add $- 1$ and $3$ .

$\frac{2}{10 b^{2} j^{- 2}}$

Step 3

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

$\frac{2 j^{2}}{10 b^{2}}$

Step 4

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 j^{2}$ .

$\frac{2 (j^{2})}{10 b^{2}}$

Cancel the common factors.

Factor $2$ out of $10 b^{2}$ .

$\frac{2 (j^{2})}{2 (5 b^{2})}$

Cancel the common factor.

$\frac{2 j^{2}}{2 (5 b^{2})}$

Rewrite the expression.

$\frac{j^{2}}{5 b^{2}}$