EXPONENT question - gmatprep

Question

Hi,

can some one help??

another question:

if I factor the 4^11 to (2^2)^11

do I add the exponents 2 and 11? or do I multiply?

Thanks,

phoenixgmat · Answer

hey,

4^11 = 2^11 * 2^11.

in such a case I could recommend, that you just try it with a calculator.
ok, you cant do that in the actual test, but in the preparation time!

MontrealLady · Answer

Thank you, but I still need an answer for the gmat question

MontrealLady · Answer

I have another similar question

Bunuel · Answer

EXPONENTS:

- You can combine exponents of the same base or same exponents only in multiplication and division

Operations involving the same exponents: 
- Keep the exponent, multiply or divide the bases

x^n*y^n=(xy) ^n

x^n/y^n=(x/y) ^n

E.g. Same exponent - multiplication
(2^3)(5^3) = 10^3
E.g. Same exponent - division
(10^2)/(5^2) = 2^2

Operations involving the same bases: 
- Keep the base, add or subtract the exponent (add for multiplication, subtract for division)

x^n*x^m=x^(n+m)

x^n/x^m=x^(n-m)

E.g. Same base - multiplication
(5^3)*(5^6) = 5^(3+6) = 5^9
E.g. Same base - division
(6^3)/(6^2) = 6^1 = 6

Operation involving powers of base: 
 (x^n)^m=x^nm

Your case: 
4^11 = (2^2)^11=2^22

Different case when:
 x^n^m=x^(n^m) AND NOT (x^n)^m

TIPS:
 x^0=1

0^n=0  n>0

x^(-n)=1/x^n

If n is an even integer, then (−1)^n = 1.
If n is an odd integer, then (−1)^n = −1.

For  x^n-y^n: 
When n is odd  x^n-y^n  is divisible by x-y
When n is even  x^n-y^n  is divisible by x+y

cdowwe · Answer

Here is what I did for Q1.

5^21 = 50,000,000,000^11

50,000,000,000^11 X 4^11=

200,000,000,000^11=

2 x 100,000,000,000^11

2x10^21

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