Precalculus Examples

$4^{x} = \sqrt[5]{64}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{64}$ as $64^{\frac{1}{5}}$ .

$4^{x} = 64^{\frac{1}{5}}$

Step 2

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

$4^{x} = 4^{3 (\frac{1}{5})}$

Step 3

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

$x = 3 (\frac{1}{5})$

Step 4

Combine $3$ and $\frac{1}{5}$ .

$x = \frac{3}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}$

Decimal Form:

$x = 0.6$