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Basic exponents/roots problems, please help

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Basic exponents/roots problems, please help [#permalink] New post 14 Jun 2009, 23:45
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1. If M = Square root 4 + Cube root 4 + Quad root 4, then the value of M is?

1) less than 3
2) 3
3) btween 3 and 4
4) 4
5) greater than 4

2. If 5^21 * 4^11 = 2 * 10^nwhat is the value of n?

1) 11
2) 21
3) 22
4) 23
5) 32

Is there any page you can recommend for learning how to deal with A^x + B^y and a^x * B^y? Im clueless regarding these.

3.

\frac{((8^2)(3^3)(2^4))}{96^2}

1) 3
2) 6
3) 9
4) 12
5) 18
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Re: Basic exponents/roots problems, please help [#permalink] New post 15 Jun 2009, 04:20
Ques 1. If M = \sqrt{4} + \sqrt[3]{4} + \sqrt[4]{4}
M = 2 + \sqrt[\frac{2}{3}]{2} + \sqrt{2}
M = 2 + \approx 1.5 + \approx 1.4

This will be greater than 4

Ques 2. 5^{21} * 4^{11} = 2 * 10^n

5^{21} * 2^{22} = 2 * 5^n * 2^n

n=21

Ques 3. \frac{(8^2)(3^3)(2^4)}{96^2}

=\frac{8^2*3^3*2^4}{3^2*2^{10}}
=\frac{2^6*3^3*2^4}{3^2*2^{10}}

=3

Last edited by humans on 15 Jun 2009, 23:47, edited 1 time in total.
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Re: Basic exponents/roots problems, please help [#permalink] New post 15 Jun 2009, 14:17
If 5^{21} \times 4^{11} = 2 \times 10^n what is the value of n?

1) 11
2) 21
3) 22
4) 23
5) 32

Asking n=?
Given

5^{21} \times 4^{11} = 2 \times 10^n

\Rightarrow 5^{21} \times (2^2)^{11} = 2 \times 10^n

\Rightarrow 5^{21} \times 2^{22} = 2 \times 10^n

\Rightarrow 5^{21} \times 2^{21} \times 2 = 2 \times 10^n

\Rightarrow (5 \times 2)^{21} \times 2 = 2 \times 10^n

\Rightarrow 10^{21} \times 2 = 2 \times 10^n

\Rightarrow 2 \times 10^{21} = 2 \times 10^n

\Rightarrow n = 21
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Re: Basic exponents/roots problems, please help [#permalink] New post 15 Jun 2009, 14:38
Expert's post
Philosophus Rex - welcome to GMATClub.

You are an active member and we are happy to see you here. Wanted to show you a few quick shortcuts to post math expressions that are easier to read for everyone, similar to how Nookway responded to your questions.

To create a math formula, most of the time all you have to do is select the expression and hit the M button (located under the B, I, U buttons in the Message Posting screen)

Here is what I did to convert your posts to math-friendly format -mostly just add an M-Tag on both sides of the expression. Feel free to contact me if you have any questions!

Code:
2. If [m]5^21 * 4^11 = 2 * 10^n[/m]what is the value of n?

Is there any page you can recommend for learning how to deal with [m]A^x + B^y and a^x * B^y[/m]? Im clueless regarding these.

3. [m][fraction]((8^2)(3^3)(2^4))/96^2[/fraction][/m]

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mathposting.jpg
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Re: Basic exponents/roots problems, please help   [#permalink] 15 Jun 2009, 14:38
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