Solve for x 4^(5x)=1/16

$4^{5 x} = \frac{1}{16}$

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

$4^{5 x} = \frac{1}{16^{1}}$

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

$4^{5 x} = 16^{- 1}$

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

$4^{5 x} = 4^{- 2}$

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

$5 x = - 2$

Divide each term in $5 x = - 2$ by $5$ and simplify.

Divide each term in $5 x = - 2$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{5}$

Decimal Form:

$x = - 0.4$