Evaluate 1/36=6^(x-3)

$\frac{1}{36} = 6^{x - 3}$

Step 1

Rewrite the equation as $6^{x - 3} = \frac{1}{36}$ .

$6^{x - 3} = \frac{1}{36}$

Step 2

Raise $36$ to the power of $1$ .

$6^{x - 3} = \frac{1}{36^{1}}$

Step 3

Move $36^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$6^{x - 3} = 36^{- 1}$

Step 4

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

$6^{x - 3} = 6^{- 2}$

Step 5

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

$x - 3 = - 2$

Step 6

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$x = - 2 + 3$

Add $- 2$ and $3$ .

$x = 1$