Solve for m 16^(m+1)=64^(-3m)

$16^{m + 1} = 64^{- 3 m}$

Step 1

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

$4^{2 (m + 1)} = 4^{3 (- 3 m)}$

Step 2

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

$2 (m + 1) = 3 (- 3 m)$

Step 3

Solve for $m$ .

Simplify $2 (m + 1)$ .

Start simplifying.

$0 + 0 + 2 (m + 1) = 3 (- 3 m)$

Simplify by adding zeros.

$2 (m + 1) = 3 (- 3 m)$

Apply the distributive property.

$2 m + 2 \cdot 1 = 3 (- 3 m)$

Multiply $2$ by $1$ .

$2 m + 2 = 3 (- 3 m)$

Multiply $- 3$ by $3$ .

$2 m + 2 = - 9 m$

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

Add $9 m$ to both sides of the equation.

$2 m + 2 + 9 m = 0$

Add $2 m$ and $9 m$ .

$11 m + 2 = 0$

Subtract $2$ from both sides of the equation.

$11 m = - 2$

Divide each term in $11 m = - 2$ by $11$ and simplify.

Divide each term in $11 m = - 2$ by $11$ .

$\frac{11 m}{11} = \frac{- 2}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 m}{11} = \frac{- 2}{11}$

Divide $m$ by $1$ .

$m = \frac{- 2}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{2}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{2}{11}$

Decimal Form:

$m = - 0.\overline{18}$