need help putting into words

• Jan 8th 2007, 06:24 AM
math619
need help putting into words
I need to show which of the two expressions is larger and explian why. I know which is the larger number,but can not put it into words to explain. Anyone have any ideas?

a) (1/2)'2 or (1/3)'3

b)(1/3)'-2 or (1/3)'-3

*Note: (1/2)'2 is "one half squared"*
• Jan 8th 2007, 07:02 AM
ThePerfectHacker
Quote:

Originally Posted by math619
I need to show which of the two expressions is larger and explian why. I know which is the larger number,but can not put it into words to explain. Anyone have any ideas?

a) (1/2)'2 or (1/3)'3

b)(1/3)'-2 or (1/3)'-3

*Note: (1/2)'2 is "one half squared"*

$(1/2)^2=1/4$
$(1/3)^2=1/9$

Now, what is larger?
Taking something and dividing it into 4 parts of equal length, or taking something dividing it into 9 parts of equal length?
Surly the first one.
Thus,
$1/4>1/9$
• Jan 8th 2007, 07:43 AM
riki_haj
Quote:

Originally Posted by math619
I need to show which of the two expressions is larger and explian why. I know which is the larger number,but can not put it into words to explain. Anyone have any ideas?

a) (1/2)'2 or (1/3)'3

b)(1/3)'-2 or (1/3)'-3

*Note: (1/2)'2 is "one half squared"*

(1/2)^2=1/4=9/36
(1/3)^2=1/9=4/36
Now you can compare, 9/36>4/36, 1/4>1/9.
• Jan 8th 2007, 10:11 AM
earboth
Quote:

Originally Posted by math619
I need to show which of the two expressions is larger and explian why. ...

b)(1/3)'-2 or (1/3)'-3

Hello,

with negative exponents you have to use the following property:

$a^{-n}=\frac{1}{a^n}$

$\left(\frac{1}{3} \right)^{-2}=\frac{1}{\left(\frac{1}{3} \right)^2}=\frac{1}{\frac{1}{9}}=9$

$\left(\frac{1}{3} \right)^{-3}=\frac{1}{\left(\frac{1}{3} \right)^3}=\frac{1}{\frac{1}{27}}=27$

Now you can compare!

EB