fractional exponents - without calculators

• April 4th 2010, 05:15 PM
calculus0
fractional exponents - without calculators
How does

2/3 * (2)^3/2 = 4/3 * root 2

i got as far as: 2/3 * root 2 ^ 3 but i cant seem to simplify.
• April 4th 2010, 05:20 PM
Anonymous1
Quote:

Originally Posted by calculus0
How does

2/3 * (2)^3/2 = 4/3 * root 2

i got as far as: 2/3 * root 2 ^ 3 but i cant seem to simplify.

well...

Are you familiar with this rule: $x^a\times x^b = x^{a+b}?$

And the fact that $x^{1/2}= \sqrt{x}?$

$\frac{2}{3} \times 2^{3/2} = \frac{2}{3}\times2^1 \times 2^{1/2} = \frac{4}{3} \sqrt{2}.$
• April 4th 2010, 05:43 PM
Wilmer
Quote:

Originally Posted by calculus0
2/3 * (2)^3/2 = 4/3 * root 2

Your equation is "wrong" due to poor bracketing; should be:
2/3 * 2^(3/2) = 4/3 * root 2

(2)^3/2 = 8/2 = 4 : kapish?
• April 4th 2010, 06:00 PM
calculus0
Thank you anonymous!
• April 4th 2010, 06:03 PM
Anonymous1
Quote:

Originally Posted by Wilmer
Your equation is "wrong" due to poor bracketing; should be:
2/3 * 2^(3/2) = 4/3 * root 2

(2)^3/2 = 8/2 = 4 : kapish?

Its just ambiguous, not wrong. For instance, MATLAB evaluates 2^3/2 as $2^{3/2}.$

• April 4th 2010, 07:05 PM
Wilmer
Quote:

Originally Posted by Anonymous1
Its just ambiguous, not wrong. For instance, MATLAB evaluates 2^3/2 as $2^{3/2}.$