Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $4$ by $- 1$ .

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

Step 5

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

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

Step 6

Subtract $4$ from $6$ .

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

Step 7

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

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

Step 8

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

$2 m = m + 2$

Step 9

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

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Step 9.1

Subtract $m$ from both sides of the equation.

$2 m - m = 2$

Step 9.2

Subtract $m$ from $2 m$ .

$m = 2$