How does one side equal the other

1. Apr 10, 2013

KTiaam

1. The problem statement, all variables and given/known data

I know this isnt exactly calculus related but it is from working out a calculus problem

I was wondering how:
(8/27) * [103/2 - (13/4)3/2]

equals

(1/27) * [80 * sqrt(10) - 13 * sqrt(13)]

3. The attempt at a solution

All i can conclude from this answer is that they multiplied 8 throughout the equation but i don't understand the rest of it, it doesn't make sense

2. Apr 10, 2013

Staff: Mentor

They didn't multiply 8 "throughout the equation." This is an expression, and they are using the distributive property like this: a(b + c) = ab + ac.

(8/27) * [103/2 - (13/4)3/2]
= 1/27 * [8 * 10 √10 - 8 * (13/4) * √(13/4)]
Can you continue from here?

3. Apr 10, 2013

Vorde

$\frac{8}{27} [10^{3/2} - (\frac{13}{4}) ^{3/2}] = (1/27) [80 \sqrt{10} - 13 \sqrt{13}]$

Remember that $x^{a/b} = \sqrt{x} ^a$ and $(\frac{a}{b}) ^y = \frac{(a^y)}{(b^y)}$
Now try distributing the 8 and using those rules.

4. Apr 10, 2013

KTiaam

i understand that part but where did the power of 3 go?

5. Apr 10, 2013

Staff: Mentor

103/2 = 101 + 1/2 = 10 * √10

6. Apr 10, 2013

KTiaam

wow am i really that dumb?

this whole time i was thinking

103/2 was equal to (√10)3

man, its been a rough day for me, thanks mark.

7. Apr 10, 2013

Vorde

By the way, it does.

10^(3/2) = (√10)^3 = (√10)*(√10)*(√10) = (√10)*(√10)^2 = (√10)*10