How does one side equal the other

[KTiaam]

Homework Statement

I know this isn't exactly calculus related but it is from working out a calculus problem

I was wondering how:
(8/27) * [10^3/2 - (13/4)^3/2]

equals

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

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

 

[Mark44]

Homework Statement

I know this isn't exactly calculus related but it is from working out a calculus problem

I was wondering how:
(8/27) * [10^3/2 - (13/4)^3/2]

equals

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

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

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

 

[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.

 

[KTiaam]

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

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

 

[Mark44]

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

10^3/2 = 10^{1 + 1/2} = 10 * √10

 

[KTiaam]

10^3/2 = 10^{1 + 1/2} = 10 * √10

wow am i really that dumb?

this whole time i was thinking

10^3/2 was equal to (√10)³

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

 

[Vorde]

wow am i really that dumb?


10^3/2 was equal to (√10)³

By the way, it does.

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