Solve for m 4^m=(2^(m+6))/16

$4^{m} = \frac{2^{m + 6}}{16}$

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

$4^{m} = \frac{2^{m + 6}}{16^{1}}$

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

$4^{m} = 2^{m + 6} \cdot 16^{- 1}$

Rewrite $16$ as $2^{4}$ .

$4^{m} = 2^{m + 6} \cdot {(2^{4})}^{- 1}$

Multiply the exponents in ${(2^{4})}^{- 1}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4^{m} = 2^{m + 6} \cdot 2^{4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$4^{m} = 2^{m + 6} \cdot 2^{- 4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4^{m} = 2^{m + 6 - 4}$

Subtract $4$ from $6$ .

$4^{m} = 2^{m + 2}$

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

$2^{2 m} = 2^{m + 2}$

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

$2 m = m + 2$

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

Subtract $m$ from both sides of the equation.

$2 m - m = 2$

Subtract $m$ from $2 m$ .

$m = 2$