Solve for b 4^(3b-3)=1/16

$4^{3 b - 3} = \frac{1}{16}$

Step 1

Raise $16$ to the power of $1$ .

$4^{3 b - 3} = \frac{1}{16^{1}}$

Step 2

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{3 b - 3} = 16^{- 1}$

Step 3

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

$4^{3 b - 3} = 4^{- 2}$

Step 4

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

$3 b - 3 = - 2$

Step 5

Solve for $b$ .

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

Add $3$ to both sides of the equation.

$3 b = - 2 + 3$

Add $- 2$ and $3$ .

$3 b = 1$

Divide each term in $3 b = 1$ by $3$ and simplify.

Divide each term in $3 b = 1$ by $3$ .

$\frac{3 b}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 b}{3} = \frac{1}{3}$

Divide $b$ by $1$ .

$b = \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{3}$

Decimal Form:

$b = 0.\overline{3}$