Question

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

Answer 1

DEFINITIONS:

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

$a^{\frac{m}{n}}$

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

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

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

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

$\sqrt[3]{18t}=(18t)^{\frac{1}{3}}$

Therefore, the answer is:

$(18t)^{\frac{1}{3}}$