Explained: "The rational exponent form of a0.4 in radical..."

remolatg

Answered question

2021-08-14

The rational exponent form of

a^{0.4}

in radical form.

comentezq

Skilled2021-08-15Added 106 answers

To determine you need

Vasquez

Expert2021-12-16Added 669 answers

Change 0.4 into a fraction.

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

$a^{\frac{10 \cdot 0.4}{10}}$

Multiply 10 by 0.4.

$a^{\frac{4}{10}}$

Cancel the common factor of 4 and 10

Factor 2 out of 4.

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

Cancel the common factors.

Factor 2 out of 10.

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$\sqrt[5]{a^{2}}$

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