Help! First year of college math! : (

C

colepoin

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Joined
Dec 7, 2011
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Alright, it's my first year of college math, and so far, I'm hating it!


Here is the problem.


(4/9) -3/2


* the -3/2 appears as an exponent on the outside of the parenthesis.*

*Both the 4/9 and the -3/2 are fractions.*



:( Please help!
 
Hello, colepoin!

If you've never had Algebra, no wonder you hate the course!

\(\displaystyle \text{Here is the problem: }\:\left(\dfrac{4}{9}\right)^{-\frac{3}{2}}\)
Click to expand...

You're expected to understand the following steps . . .

\(\displaystyle \left(\dfrac{4}{9}\right)^{-\frac{3}{2}} \;=\;\dfrac{1}{\left(\dfrac{4}{9}\right)^{\frac{3}{2}}} \;=\;\dfrac{1}{\left(\sqrt{\dfrac{4}{9}}\right)^3} \;=\;\dfrac{1}{\left(\dfrac{\sqrt{4}}{\sqrt{9}}}\right)^3} \;=\;\dfrac{1}{\left(\dfrac{2}{3}\right)^3} \;=\;\dfrac{\;\;\;1\;\;\;}{\dfrac{2^3}{3^3}} \;=\) .\(\displaystyle \dfrac{\;\;\;1\;\;\;}{\dfrac{8}{27}} \;=\;\dfrac{27}{8}\)
 
We text exponents using the caret symbol ^ (shifted six, on most keyboards).

When typing an exponent that's more than one character, we enclose the exponent inside grouping symbols.

(4/9)^(-3/2)

PS: This is not college-level math; most people learn this in early high school -- and then forget! :)
 
An alternative approach with negative exponents (used recently by JeffM) eliminates the reciprocal right away.

(4/9)^(-3/2)

(9/4)^(3/2)

(3/2)^3

27/8
 
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