Math Help - 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 $2^{3/2}.$