Algebra Examples

$\frac{1}{\sqrt[5]{216}} = 6^{x}$

Step 1

Rewrite the equation as $6^{x} = \frac{1}{\sqrt[5]{216}}$ .

$6^{x} = \frac{1}{\sqrt[5]{216}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{216}$ as $216^{\frac{1}{5}}$ .

$6^{x} = \frac{1}{216^{\frac{1}{5}}}$

Step 3

Move $216^{\frac{1}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$6^{x} = 216^{- \frac{1}{5}}$

Step 4

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

$6^{x} = 6^{3 (- \frac{1}{5})}$

Step 5

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

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

Step 6

Simplify $3 (- \frac{1}{5})$ .

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Step 6.1

Multiply $3 (- \frac{1}{5})$ .

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Step 6.1.1

Multiply $- 1$ by $3$ .

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

Step 6.1.2

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

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

Step 6.2

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.6$