fractional exponents - without calculators

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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 $2^{3/2}.$

So, MATLAB says your wrong.
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 $2^{3/2}.$
So, MATLAB says your wrong.

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
addition and subtraction

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