Solve for x 4^(2x)*1/16=4^(6x+18)

$4^{2 x} \cdot \frac{1}{16} = 4^{6 x + 18}$

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

$4^{2 x} \cdot \frac{1}{16^{1}} = 4^{6 x + 18}$

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

$4^{2 x} \cdot 16^{- 1} = 4^{6 x + 18}$

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

${(2^{2})}^{2 x} \cdot 16^{- 1} = 4^{6 x + 18}$

Multiply the exponents in ${(2^{2})}^{2 x}$ .

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

$2^{2 (2 x)} \cdot 16^{- 1} = 4^{6 x + 18}$

Multiply $2$ by $2$ .

$2^{4 x} \cdot 16^{- 1} = 4^{6 x + 18}$

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

$2^{4 x} \cdot {(2^{4})}^{- 1} = 4^{6 x + 18}$

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

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

$2^{4 x} \cdot 2^{4 \cdot - 1} = 4^{6 x + 18}$

Multiply $4$ by $- 1$ .

$2^{4 x} \cdot 2^{- 4} = 4^{6 x + 18}$

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

$2^{4 x - 4} = 4^{6 x + 18}$

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

$2^{4 x - 4} = 2^{2 (6 x + 18)}$

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

$4 x - 4 = 2 (6 x + 18)$

Solve for $x$ .

Simplify $2 (6 x + 18)$ .

Rewrite.

$4 x - 4 = 0 + 0 + 2 (6 x + 18)$

Simplify by adding zeros.

$4 x - 4 = 2 (6 x + 18)$

Apply the distributive property.

$4 x - 4 = 2 (6 x) + 2 \cdot 18$

Multiply.

Multiply $6$ by $2$ .

$4 x - 4 = 12 x + 2 \cdot 18$

Multiply $2$ by $18$ .

$4 x - 4 = 12 x + 36$

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

Subtract $12 x$ from both sides of the equation.

$4 x - 4 - 12 x = 36$

Subtract $12 x$ from $4 x$ .

$- 8 x - 4 = 36$

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

Add $4$ to both sides of the equation.

$- 8 x = 36 + 4$

Add $36$ and $4$ .

$- 8 x = 40$

Divide each term in $- 8 x = 40$ by $- 8$ and simplify.

Divide each term in $- 8 x = 40$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{40}{- 8}$

Divide $x$ by $1$ .

$x = \frac{40}{- 8}$

Simplify the right side.

Divide $40$ by $- 8$ .

$x = - 5$

Solve for x 4^(2x)*1/16=4^(6x+18)

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