Solve for n 2^(9n-11)=1/16

$2^{9 n - 11} = \frac{1}{16}$

Step 1

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

$2^{9 n - 11} = \frac{1}{16^{1}}$

Step 2

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

$2^{9 n - 11} = 16^{- 1}$

Step 3

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

$2^{9 n - 11} = 2^{- 4}$

Step 4

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

$9 n - 11 = - 4$

Step 5

Solve for $n$ .

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

Add $11$ to both sides of the equation.

$9 n = - 4 + 11$

Add $- 4$ and $11$ .

$9 n = 7$

Divide each term in $9 n = 7$ by $9$ and simplify.

Divide each term in $9 n = 7$ by $9$ .

$\frac{9 n}{9} = \frac{7}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 n}{9} = \frac{7}{9}$

Divide $n$ by $1$ .

$n = \frac{7}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = \frac{7}{9}$

Decimal Form:

$n = 0.\overline{7}$