Problem Solving

Hi there,

I was wondering if someone could help me determine an efficient approach to solving problem-solving questions that ask for what the exponent of a product would be in a mathematical equation. For instance, here is a question that illustrates my concern:

QUESTION

If 5^21 x 4^11 = 2 x 10^n, what is n?
a) 11
b) 21 (answer)
c) 22
d) 23
e) 32

Should I simplify 4^11 somehow/try to simplify each term to the same "base" value? Totally confused with such questions that deal with very large exponents...


Would appreciate any help you have to offer!

Thank you
Krithika

This was my way of doing it stepwise :

5^21 * 4^11

5^10 * 5^11 * 4^11

5^10 * 20^11

5^10 * 2^11 * 10^11

5^10 * 2^10 * 2^1 10^11

10^10 * 2^1 * 10^11

2^1 * 10^21

hence n is 21

Even simpler is :

5^21 * 4^11

5^11 * 5^10 * 2^11 * 2^10 * 2^1

10^11 * 10^10 * 2^1

10^21 * 2^1

Don't trust anyone who doesn't use superscripts

5²¹ * 4¹¹ = 2 * 10�

5²¹ * (2²)¹¹ = 2 * (2*5)�

5²¹ * 2²² = 2¹ * 2� * 5�

We have to have the same exponent on the 5s, so n = 21.