Algebra Examples

$2 {(2)}^{x} = \frac{1}{8}$

Step 1

Raise $8$ to the power of $1$ .

$2 \cdot 2^{x} = \frac{1}{8^{1}}$

Step 2

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

$2 \cdot 2^{x} = 8^{- 1}$

Step 3

Multiply $2$ by $2^{x}$ .

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Step 3.1

Raise $2$ to the power of $1$ .

$2^{1} \cdot 2^{x} = 8^{- 1}$

Step 3.2

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

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

Step 4

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

$2^{1 + x} = 2^{- 3}$

Step 5

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

$1 + x = - 3$

Step 6

Move all terms not containing $x$ to the right side of the equation.

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Step 6.1

Subtract $1$ from both sides of the equation.

$x = - 3 - 1$

Step 6.2

Subtract $1$ from $- 3$ .

$x = - 4$