Solve for x (4^6)/(4^x)=4^0

$\frac{4^{6}}{4^{x}} = 4^{0}$

Step 1

Move $4^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{6} \cdot 4^{- x} = 4^{0}$

Step 2

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

$4^{6 - x} = 4^{0}$

Step 3

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

$6 - x = 0$

Step 4

Solve for $x$ .

Subtract $6$ from both sides of the equation.

$- x = - 6$

Divide each term in $- x = - 6$ by $- 1$ and simplify.

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x = 6$