PS: Exponents

Question

5^21 x 4^11 = 2x10^n

Solve for n, and please demonstrate your method.

ArvGMAT · Answer

n = 21
2*10^n can be written as
2*5^n*2^n
=2^(n+1)*5^n

equate powers of 5 gives n=21

kirakira · Answer

5^21 x 4^11 = 5^21 x (2^2)^11 = 5^21 x 2^22 = 2 (5^21 x 2^21) = 2 (2 x 5)^n

=> n = 21

sludge · Answer

Shoot those problems are always so easy in retrospect

bkk145 · Answer

I think many people confuse (x^y)^z as x^(y+z) which is incorrect.
(x^y)^z = x^(yz)
(x^y) * (x^z) = x^(y+z)
Not sure if this is your confusion, but I have seen many people switched the two...
Good luck.

grad_mba · Answer

The LHS can be rewritten as :

(10/2)^21 x 2^22 => 10^21 x 2 

n = 21

vay · Answer

n = 21

5^21 * 4^11 = 5^21 * 2^22

= 2 * 5^21 * 2^21
= 2 * 10^21

===>> n = 21

PS: Exponents

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