Question

Please show your work, and explain how to solve for other exponents like this.

Answer 1

Explanation:

The bases are like (they're both 2's) so the rule for quotients is that we subtract the lower exponent from the upper:

`2^{(3)/(4)-(1)/(2)}` but we need a common denominator so

`2^{(3)/(4)-(2)/(4)}` which simplifies to

`2^{(1)/(4)}`

In a rational exponent, the denominator serves as the index of the radical (the little number that sits in the crook of the radical sign) and the numerator serves as the power on the base. Rewriting our answer as a radical then:

`\sqrt[4]{2^1}` which is the same thing as

`\sqrt[4]{2}`