Subracting numbers with fractional exponents

[synapticzero]

2^(5/2) - 2^(3/2)

I know that you can convert to this:

sqrt 2^5 - sqrt 2^3

but I'm not sure what to do at this point.

The answer is 2^(2/3). Please explain how to get that answer.

 

[masters]

2^(5/2) - 2^(3/2)

I know that you can convert to this:

sqrt 2^5 - sqrt 2^3

but I'm not sure what to do at this point.

The answer is 2^(2/3). Please explain how to get that answer.

I kinda disagree with your answer. Here's why.

\(\displaystyle 2^{\frac{5}{2}}-2^{\frac{3}{2}}=\sqrt{2^5}-\sqrt{2^3}=4\sqrt{2}-2\sqrt{2}=2\sqrt{2}=2^{\frac{2}{2}} \cdot 2^{\frac{1}{2}}=2^\frac{3}{2}}\)

 

[synapticzero]

thank you!

 

[soroban]

Hello, synapticzero!

\(\displaystyle \text{Simplify: }\:2^{\frac{5}{2}} - 2^{\frac{3}{2}}\)

\(\displaystyle \text{Factor out }2^{\frac{3}{2}}\!:\quad2^{\frac{3}{2}}\cdot \bigg[2^1 - 1\bigg] \;=\;2^{\frac{3}{2}}\cdot(2 - 1) \;=\;2^{\frac{3}{2}}\)