Simplify (8e^-4f^-2)/(18ef^-5)

$\frac{8 e^{- 4} f^{- 2}}{18 e f^{- 5}}$

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

$\frac{8 f^{- 2}}{18 e f^{- 5} e^{4}}$

Multiply $e$ by $e^{4}$ by adding the exponents.

Move $e^{4}$ .

$\frac{8 f^{- 2}}{18 (e^{4} e) f^{- 5}}$

Multiply $e^{4}$ by $e$ .

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

$\frac{8 f^{- 2}}{18 (e^{4} e^{1}) f^{- 5}}$

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

$\frac{8 f^{- 2}}{18 e^{4 + 1} f^{- 5}}$

Add $4$ and $1$ .

$\frac{8 f^{- 2}}{18 e^{5} f^{- 5}}$

Move $f^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{8 f^{- 2} f^{5}}{18 e^{5}}$

Multiply $f^{- 2}$ by $f^{5}$ by adding the exponents.

Move $f^{5}$ .

$\frac{8 (f^{5} f^{- 2})}{18 e^{5}}$

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

$\frac{8 f^{5 - 2}}{18 e^{5}}$

Subtract $2$ from $5$ .

$\frac{8 f^{3}}{18 e^{5}}$

Cancel the common factor of $8$ and $18$ .

Factor $2$ out of $8 f^{3}$ .

$\frac{2 (4 f^{3})}{18 e^{5}}$

Cancel the common factors.

Factor $2$ out of $18 e^{5}$ .

$\frac{2 (4 f^{3})}{2 (9 e^{5})}$

Cancel the common factor.

$\frac{2 (4 f^{3})}{2 (9 e^{5})}$

Rewrite the expression.

$\frac{4 f^{3}}{9 e^{5}}$