Algebra Examples

$128 = 4^{2 x} \cdot 2^{x}$

Step 1

Rewrite the equation as $4^{2 x} \cdot 2^{x} = 128$ .

$4^{2 x} \cdot 2^{x} = 128$

Step 2

Rewrite $4$ as $2^{2}$ .

${(2^{2})}^{2 x} \cdot 2^{x} = 128$

Step 3

Multiply the exponents in ${(2^{2})}^{2 x}$ .

Tap for more steps...

Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{2 (2 x)} \cdot 2^{x} = 128$

Step 3.2

Multiply $2$ by $2$ .

$2^{4 x} \cdot 2^{x} = 128$

Step 4

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

$2^{4 x + x} = 128$

Step 5

Add $4 x$ and $x$ .

$2^{5 x} = 128$

Step 6

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

$2^{5 x} = 2^{7}$

Step 7

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

$5 x = 7$

Step 8

Divide each term in $5 x = 7$ by $5$ and simplify.

Tap for more steps...

Step 8.1

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Step 8.2

Simplify the left side.

Tap for more steps...

Step 8.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 8.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{5}$

Decimal Form:

$x = 1.4$

Mixed Number Form:

$x = 1 \frac{2}{5}$