Solve for x 8^x*8^(-x-1)=1/64

$8^{x} \cdot 8^{- x - 1} = \frac{1}{64}$

Step 1

Raise $64$ to the power of $1$ .

$8^{x} \cdot 8^{- x - 1} = \frac{1}{64^{1}}$

Step 2

Move $64^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$8^{x} \cdot 8^{- x - 1} = 64^{- 1}$

Step 3

Multiply $8^{x}$ by $8^{- x - 1}$ by adding the exponents.

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

$8^{x - x - 1} = 64^{- 1}$

Subtract $x$ from $x$ .

$8^{0 - 1} = 64^{- 1}$

Subtract $1$ from $0$ .

$8^{- 1} = 64^{- 1}$

Step 4

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

$8^{- 1} = 8^{- 2}$

Step 5

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

$- 1 = - 2$

Step 6

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

No solution