Prime factorization of a number

Hello. What have you tried or thought about with this exercise? The brute-force method is to evaluate the given expression, followed by factoring the result.

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mmm4444bot said:
Hello. What have you tried or thought about with this exercise? The brute-force method is to evaluate the given expression, followed by factoring the result.

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
www.freemathhelp.com
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Hi, i tried the brute method :LOL:. So i was thinking what if the expression inside the parentheses is like REALLY big then what? There must a faster way to solve this. That's why i posted it here. I got the right answer which is option (b) after evaluating the expression.
 
Qwertyuiop[] said:
Hi, I need help with this question.

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Start by factoring [imath]3^2[/imath] out of [imath]3^4+3^2[/imath], and writing this number in factored form (or just evaluate it and factor, since it isn't big).

Then you just have a product of factors, and can apply rules for exponents. Give it a try, and show us an attempt, so we can help more.
 
3^4 + 3^2 = 81 + 9 = 90 = 9*10 = 3^2*2*5. So what is the prime factorization of (3^4 + 3^2)^3.
Hint: It is the prime factorization of (3^2*2*5)^3
 
Qwertyuiop[] said:
Hi, i tried the brute method :LOL:. So i was thinking what if the expression inside the parentheses is like REALLY big then what? There must a faster way to solve this. That's why i posted it here. I got the right answer which is option (b) after evaluating the expression.
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Brute force is in the eyes of the beholder. Here is my solution, with no large numbers
[imath](3^4+3^2)^3=(3^6)(3^2+1)^3=(3^6)(10)^3=2^3 \cdot 3^6\cdot 5^3 [/imath]
Thus [imath]{\bf\large(3^4+3^2)^3\cdot 5^2=2^3 \cdot 3^6\cdot 5^5} [/imath]

[imath][/imath][imath][/imath][imath][/imath][imath][/imath]
 
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