Solve for x (1/8)^(3x)=64

${(\frac{1}{8})}^{3 x} = 64$

Step 1

Apply the product rule to $\frac{1}{8}$ .

$\frac{1^{3 x}}{8^{3 x}} = 64$

Step 2

One to any power is one.

$\frac{1}{8^{3 x}} = 64$

Step 3

Move $8^{3 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$8^{- 3 x} = 64$

Step 4

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

$8^{- 3 x} = 8^{2}$

Step 5

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

$- 3 x = 2$

Step 6

Divide each term in $- 3 x = 2$ by $- 3$ and simplify.

Divide each term in $- 3 x = 2$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{2}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{2}{- 3}$

Divide $x$ by $1$ .

$x = \frac{2}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}$

Decimal Form:

$x = - 0.\overline{6}$