Simplify (3^-1)÷(3^4)

$3^{- 1} \div 3^{4}$

Rewrite the division as a fraction.

$\frac{3^{- 1}}{3^{4}}$

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

$\frac{1}{3^{4} \cdot 3}$

Multiply $3^{4}$ by $3$ by adding the exponents.

Multiply $3^{4}$ by $3$ .

Raise $3$ to the power of $1$ .

$\frac{1}{3^{4} \cdot 3^{1}}$

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

$\frac{1}{3^{4 + 1}}$

Add $4$ and $1$ .

$\frac{1}{3^{5}}$

Raise $3$ to the power of $5$ .

$\frac{1}{243}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{243}$

Decimal Form:

$0.00411522 \dots$