Question

Convert this expression from radical to rational form.

(would be grateful for your help :))

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Answer 1

a^(3/4)

Explanation:

You want to use a rational exponent to describe √(√(a³)).

Square root

The square root can be represented by an exponent of 1/2.

This means the expression is can be simplified to ...

`\sqrt{√(a^3)}=\sqrt{(a^3)^(1)/(2)}=\sqrt{a^(3)/(2)}=(a^(3)/(2))^(1)/(2)=\boxed{a^(3)/(4)}`

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Additional comment

The rule of exponents in play here is (a^b)^c = a^(bc).

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