Simplify (9^-3)/(9^12)

$\frac{9^{- 3}}{9^{12}}$

Step 1

Move $9^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{9^{12} \cdot 9^{3}}$

Step 2

Multiply $9^{12}$ by $9^{3}$ by adding the exponents.

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

$\frac{1}{9^{12 + 3}}$

Add $12$ and $3$ .

$\frac{1}{9^{15}}$

Step 3

Raise $9$ to the power of $15$ .

$\frac{1}{205891132094649}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{205891132094649}$

Decimal Form:

$4.85693574 \cdot 10^{- 15}$