Simplify (d^-2e^3)/(e^-5d^7)

$\frac{d^{- 2} e^{3}}{e^{- 5} d^{7}}$

Step 1

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

$\frac{e^{3}}{e^{- 5} d^{7} d^{2}}$

Step 2

Multiply $d^{7}$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$\frac{e^{3}}{e^{- 5} (d^{2} d^{7})}$

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

$\frac{e^{3}}{e^{- 5} d^{2 + 7}}$

Add $2$ and $7$ .

$\frac{e^{3}}{e^{- 5} d^{9}}$

Step 3

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

$\frac{e^{3} e^{5}}{d^{9}}$

Step 4

Multiply $e^{3}$ by $e^{5}$ by adding the exponents.

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

$\frac{e^{3 + 5}}{d^{9}}$

Add $3$ and $5$ .

$\frac{e^{8}}{d^{9}}$