Algebra Examples

$4^{- 2 x} \cdot 4^{x} = 64$

Step 1

Subtract $64$ from both sides of the equation.

$4^{- 2 x} \cdot 4^{x} - 64 = 0$

Step 2

Multiply $4^{- 2 x}$ by $4^{x}$ by adding the exponents.

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Step 2.1

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

$4^{- 2 x + x} - 64 = 0$

Step 2.2

Add $- 2 x$ and $x$ .

$4^{- x} - 64 = 0$

Step 3

Add $64$ to both sides of the equation.

$4^{- x} = 64$

Step 4

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

$4^{- x} = 4^{3}$

Step 5

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

$- x = 3$

Step 6

Divide each term in $- x = 3$ by $- 1$ and simplify.

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Step 6.1

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Step 6.2.2

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $3$ by $- 1$ .

$x = - 3$