Solve for x (1/12)^(-2x)*12^(-2x+2)=12

${(\frac{1}{12})}^{- 2 x} \cdot 12^{- 2 x + 2} = 12$

Step 1

Apply the product rule to $\frac{1}{12}$ .

$\frac{1^{- 2 x}}{12^{- 2 x}} \cdot 12^{- 2 x + 2} = 12$

Step 2

One to any power is one.

$\frac{1}{12^{- 2 x}} \cdot 12^{- 2 x + 2} = 12$

Step 3

Move $12^{- 2 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$12^{2 x} \cdot 12^{- 2 x + 2} = 12$

Step 4

Multiply $12^{2 x}$ by $12^{- 2 x + 2}$ by adding the exponents.

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

$12^{2 x - 2 x + 2} = 12$

Subtract $2 x$ from $2 x$ .

$12^{0 + 2} = 12$

Add $0$ and $2$ .

$12^{2} = 12$

Step 5

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

$12^{2} = 12^{1}$

Step 6

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

$2 = 1$

Step 7

Since $2 \neq 1$ , there are no solutions.

No solution