Algebra Examples

$\sqrt[6]{49} = 7^{x}$

Step 1

Rewrite the equation as $7^{x} = \sqrt[6]{49}$ .

$7^{x} = \sqrt[6]{49}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{49}$ as $49^{\frac{1}{6}}$ .

$7^{x} = 49^{\frac{1}{6}}$

Step 3

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

$7^{x} = 7^{2 (\frac{1}{6})}$

Step 4

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

$x = 2 (\frac{1}{6})$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $6$ .

$x = 2 \frac{1}{2 (3)}$

Step 5.2

Cancel the common factor.

$x = 2 \frac{1}{2 \cdot 3}$

Step 5.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$