Algebra Examples

$2^{x} = 2 \sqrt{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

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

Step 2

Multiply $2$ by $2^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

Multiply $2$ by $2^{\frac{1}{2}}$ .

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Step 2.1.1

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

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

Step 2.1.2

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

$2^{x} = 2^{1 + \frac{1}{2}}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$2^{x} = 2^{\frac{2}{2} + \frac{1}{2}}$

Step 2.3

Combine the numerators over the common denominator.

$2^{x} = 2^{\frac{2 + 1}{2}}$

Step 2.4

Add $2$ and $1$ .

$2^{x} = 2^{\frac{3}{2}}$

Step 3

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

$x = \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

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