Simplify 3^-4+3^-1

$3^{- 4} + 3^{- 1}$

Step 1

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Raise $3$ to the power of $4$ .

$\frac{1}{81} + 3^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{81} + \frac{1}{3}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{1}{81} + \frac{1}{3} \cdot \frac{27}{27}$

Step 3

Write each expression with a common denominator of $81$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{27}{27}$ .

$\frac{1}{81} + \frac{27}{3 \cdot 27}$

Multiply $3$ by $27$ .

$\frac{1}{81} + \frac{27}{81}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 27}{81}$

Step 5

Add $1$ and $27$ .

$\frac{28}{81}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{28}{81}$

Decimal Form:

$0.34567901 \dots$