Question

Pleases solve and explain : 2^(5/2) - 2^(3/2) =

Answer 1

Ok, First tell me.. What is \[2^\frac{4}{2} = ?\]

Answer 2

I forget the rules of exponents.

Answer 3

Well, what is

\[\frac{4}{2} = ?\]

Answer 4

I forget the rules of exponents.

Answer 5

2

Answer 6

Right. So \[2^\frac{4}{2} = 2^2 = ?\]

Answer 7

I forget the rules of exponents.

Answer 8

But the exponents are 5/2 and 3/2. What does 4/2 have to do with the equation?

Answer 9

Well that's a good question..
But we know that \(\frac{5}{2} = \frac{4}{2} + \frac{1}{2}\)
And \(\frac{3}{2} = \frac{2}{2}+ \frac{1}{2}\)

Right?

And we know that \[a^{b+c} = a^b\cdot a^c\]

Can we put these things together somehow?

Answer 10

I forget the rules of exponents.

Answer 11

5/2 also = 3/2+2/2 . And I've lost you on the following equation. But I believe that is one of the rules. Please continue.

Answer 12

The last equation is a very important rule of exponents. When you multiply two powers of the same base you add their exponents. We can also do this in reverse.

Answer 13

So:
\[2^\frac{5}{2} - 2^\frac{3}{2}\]\[=2^\frac{4}{2}\cdot 2^\frac{1}{2} - 2^\frac{2}{2}\cdot 2^\frac{1}{2} \]

Answer 14

\[2^{\frac{4}{2}+\frac{1}{2}}-2^{\frac{2}{2}+\frac{1}{2}}\]
so this is your equation
see if you can simplify this

Answer 15

lol go polpak!

Answer 16

Sorry yes, Myinin's expression is the step you should have in between my two.

Answer 17

omg i said equation lol

Answer 18

yes it is an expression

Answer 19

rae what is the very next step after polpak's expression?