Evaluate 3^(2a)=3^(-a)

$3^{2 a} = 3^{- a}$

Step 1

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

$3^{2 a} = 3^{- a}$

Step 2

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

$2 a = - a$

Step 3

Solve for $a$ .

Move all terms containing $a$ to the left side of the equation.

Add $a$ to both sides of the equation.

$2 a + a = 0$

Add $2 a$ and $a$ .

$3 a = 0$

Divide each term in $3 a = 0$ by $3$ and simplify.

Divide each term in $3 a = 0$ by $3$ .

$\frac{3 a}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{0}{3}$

Divide $a$ by $1$ .

$a = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$a = 0$