# Thread: fractional exponents - without calculators

1. ## 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.

2. 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 $x^{1/2}= \sqrt{x}?$

$\frac{2}{3} \times 2^{3/2} = \frac{2}{3}\times2^1 \times 2^{1/2} = \frac{4}{3} \sqrt{2}.$

3. 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?

4. Thank you anonymous!

5. 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 $2^{3/2}.$

6. Originally Posted by Anonymous1
Its just ambiguous, not wrong. For instance, MATLAB evaluates 2^3/2 as $2^{3/2}.$
MATLAB can say anything it wants, I care not;
BUT 2^3/2 = 8/2 = 4

The standard order of operations.
The standard order of operations, or precedence, is expressed in the following chart.
exponents and roots
multiplication and division

7. ## Re: fractional exponents - without calculators

And that is why parentheses (or better yet mathematical formatting with tools like latex) are used. It would have been much better if the original formula was expressed as $\frac{2}{3} * (2)^\frac{3}{2} = \frac{4}{3} * \sqrt{2}$.

Also, note the spacing in the original formula. a multiplication is set off by spaces on either side. Wouldn't division (if that was intended) be similarly set off, like 2/3 * (2)^2 / 3 = 4/3 * root 2? My guess is by NOT using the extra spaces, the originator was attempting to indicate what was likely shown as a fraction in his text. Yes fractions are division and you do execute the order of operations correctly, but a better use of the forum would be to answer the problem as intended (and then point out the error), rather than critique formatting.

Plus the subject line states clearly that the problem concerns fractional exponents!

8. ## Re: fractional exponents - without calculators

something tells me calculus0 has moved on in the intervening 6 years....

10. ## Re: fractional exponents - without calculators

OOOPS. Didn't catch the date. Why I am a N00B, for sure.

11. ## Re: fractional exponents - without calculators

WARNING: Beer soaked rambling/opinion/observation/reckoning ahead. Would be readers can take it seriously or take it with a grain of salt. In no event shall the wandering quixotic math knight-errant Sir jonah in his inebriated state (usually in his dead tired but mentally revived inebriated state) be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his "enhanced" beer (and tequila/absinthe) powered views.
Originally Posted by ChuckCaldwell
OOOPS. Didn't catch the date. Why I am a N00B, for sure.
No worries Sir Chuck.
Your contribution, late as it, is still very much appreciated.
Especially appreciated was my old friend Sir Denis' delightful caffeine soaked arguments roughly 5 or 6 years ago.

12. ## Re: fractional exponents - without calculators

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