Solve for r 3^(-3r)=3^5

$3^{- 3 r} = 3^{5}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$3^{- 3 r} = 3^{5}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$- 3 r = 5$

Step 3

Divide each term in $- 3 r = 5$ by $- 3$ and simplify.

Divide each term in $- 3 r = 5$ by $- 3$ .

$\frac{- 3 r}{- 3} = \frac{5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 r}{- 3} = \frac{5}{- 3}$

Divide $r$ by $1$ .

$r = \frac{5}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$r = - \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{5}{3}$

Decimal Form:

$r = - 1.\overline{6}$

Mixed Number Form:

$r = - 1 \frac{2}{3}$