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exponents problem

by gmattesttaker2 » Sat Jul 21, 2012 10:26 am
Hello,

Sorry if this is a trivial question. But I was just wondering how to solve this:

(4th root of (x^3)).(x^3)^(1/4) = [spoiler]x^(3/4)[/spoiler]


My solution was as follows:
( (x^3)^(1/4) ).( (x^3)^(1/4) ) = (x^(3/4)).(x^(3/4)) = x^(9/16) which is in-correct.


Can you please help? This is from P. 121, MGMAT Algebra Strategy Guide (5th edition). Thanks a lot.


Best Regards,
Sri
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by theCEO » Sat Jul 21, 2012 11:33 am
x^a . x^a = x ^(a+a) = x ^2a

In your calculation you multiplied the exponents as oppose to adding them
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by eagleeye » Sat Jul 21, 2012 11:48 am
gmattesttaker2 wrote:Hello,

Sorry if this is a trivial question. But I was just wondering how to solve this:

(4th root of (x^3)).(x^3)^(1/4) = [spoiler]x^(3/4)[/spoiler]


My solution was as follows:
( (x^3)^(1/4) ).( (x^3)^(1/4) ) = (x^(3/4)).(x^(3/4)) = x^(9/16) which is in-correct.


Can you please help? This is from P. 121, MGMAT Algebra Strategy Guide (5th edition). Thanks a lot.


Best Regards,
Sri
I don't understand the question you are asking, however I did identify a problem with your solution.

x^3/4 * x^3/4 = x^(3/4+3/4) = x^(6/4) = x^3/2.

Just remember these four things when doing exponent problems:

1. x^a/x^b = x^(a-b) (Example (x^3)/(x^-1/5) = x^(3-(-1/5) = x^(3+1/5) = x^(16/5))

2. x^a * x^b = x^(a+b) (Example (x^-2.4) * x^(1.6) = x^(-2.4+1.6) = x^(-0.8))

3. nth root of x = x^(1/n) (Example 7th root of x = x^(1/7)

4. (x^a)^b = x^(a*b) (Example (x^3)^(1/4) = x^(3/4) )

Cheers!
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by gmattesttaker2 » Sat Jul 21, 2012 12:58 pm
eagleeye wrote:
gmattesttaker2 wrote:Hello,

Sorry if this is a trivial question. But I was just wondering how to solve this:

(4th root of (x^3)).(x^3)^(1/4) = [spoiler]x^(3/4)[/spoiler]


My solution was as follows:
( (x^3)^(1/4) ).( (x^3)^(1/4) ) = (x^(3/4)).(x^(3/4)) = x^(9/16) which is in-correct.


Can you please help? This is from P. 121, MGMAT Algebra Strategy Guide (5th edition). Thanks a lot.


Best Regards,
Sri
I don't understand the question you are asking, however I did identify a problem with your solution.

x^3/4 * x^3/4 = x^(3/4+3/4) = x^(6/4) = x^3/2.

Just remember these four things when doing exponent problems:

1. x^a/x^b = x^(a-b) (Example (x^3)/(x^-1/5) = x^(3-(-1/5) = x^(3+1/5) = x^(16/5))

2. x^a * x^b = x^(a+b) (Example (x^-2.4) * x^(1.6) = x^(-2.4+1.6) = x^(-0.8))

3. nth root of x = x^(1/n) (Example 7th root of x = x^(1/7)

4. (x^a)^b = x^(a*b) (Example (x^3)^(1/4) = x^(3/4) )

Cheers!

Hello Eagleeye,

Thanks for the detailed explanation and for providing all the examples. Many thanks again.

Best Regards,
Sri
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