Question

Rewrite the radical as a rational exponent. the cube root of 2 to the seventh power

Answer 1

`2^{(7)/(3)}`

Explanation:

The formula to change a radical to rational (fractional) exponent is given below:

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

It means that the denominator of the fraction (in the rational exponent) goes OUTSIDE the root sign and the numerator goes as power to the number.

Using this, we can write
`\sqrt[3]{2^(7)}` as
`2^{(7)/(3)}`

Thus the rational exponent from is given by
`2^{(7)/(3)}`

Answer 2

In converting the radical expression of a rational exponent of a rational number. First is to rewrite its form into fractional exponent and giving the answer of 2 to the power 7  over 3 and i hope this could add the knowledge of your learning, have a nice day.