Algebra Examples

$a^{1.5}$

Change $1.5$ into a fraction.

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

$a^{\frac{10 \cdot 1.5}{10}}$

Multiply $10$ by $1.5$ .

$a^{\frac{15}{10}}$

Cancel the common factor of $15$ and $10$ .

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Factor $5$ out of $15$ .

$a^{\frac{5 (3)}{10}}$

Cancel the common factors.

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Factor $5$ out of $10$ .

$a^{\frac{5 \cdot 3}{5 \cdot 2}}$

Cancel the common factor.

$a^{\frac{5 \cdot 3}{5 \cdot 2}}$

Rewrite the expression.

$a^{\frac{3}{2}}$

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

$\sqrt{a^{3}}$