Algebra Examples

$a^{- 1.6}$

Step 1

Change $- 1.6$ into a fraction.

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Step 1.1

Multiply by $\frac{10}{10}$ to remove the decimal.

$a^{\frac{10 \cdot - 1.6}{10}}$

Step 1.2

Multiply $10$ by $- 1.6$ .

$a^{\frac{- 16}{10}}$

Step 1.3

Move the negative in front of the fraction.

$a^{- \frac{16}{10}}$

Step 1.4

Cancel the common factor of $16$ and $10$ .

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Step 1.4.1

Factor $2$ out of $16$ .

$a^{- \frac{2 (8)}{10}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $2$ out of $10$ .

$a^{- \frac{2 \cdot 8}{2 \cdot 5}}$

Step 1.4.2.2

Cancel the common factor.

$a^{- \frac{2 \cdot 8}{2 \cdot 5}}$

Step 1.4.2.3

Rewrite the expression.

$a^{- \frac{8}{5}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{\frac{8}{5}}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{1}{\sqrt[5]{a^{8}}}$