Question

How do I write 3√18t using rational exponents?

Answer 1

DEFINITIONS:

Rational Exponents are also called Fractional Exponents. Consider the expression below:

`a^{(m)/(n)}`

The fractional exponent m/n indicates a radical with index n and exponent m, such that

`a^{(m)/(n)}=\sqrt[n]{a^m}`

SOLUTION TO THE QUESTION:

The question is given to be:

`\sqrt[3]{18t}`

Applying the rule of exponents we have stated earlier, we can write out the expression to be:

where, in our case

`\begin{gathered} m=1 \\ n=3 \end{gathered}`

`\sqrt[3]{18t}=(18t)^{(1)/(3)}`

Therefore, the answer is:

`(18t)^{(1)/(3)}`