Question

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

Answer 1

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

\sqrt{2^5} - \sqrt{2^3} =

4\sqrt{2} - 2\sqrt{2} =

2\sqrt{2}

Explanation:

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

2^(5/2)= \sqrt[2]{x^5}

2^(3/2)= \sqrt[2]{x^3}

Answer 2

x^(m/n)=
`\sqrt[n]{x^m}`
2^(5/2)=
`\sqrt[2]{x^5}`
2^(3/2)=
`\sqrt[2]{x^3}`

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

`√(2^5) - √(2^3)`=

`4√(2) - 2√(2)`=

`2√(2)`