5^m * 4^18 = 2*10^35
5^m * 2^36 = 2*2^35 * 5^35
5^m * 2^36 = 2^36 * 5^35
compare both the sides
m=35
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gmat prep -- powers question
Source: Beat The GMAT — Problem Solving |
Key to problems like these are trying to get the bases and exponents on the unknown variable value side to match up to the other side.
Let me explain
1/5 ^ m 1/4 ^ 18 = 1/2 * 1/10 ^ 35
= 1/5 ^ m 1/2 ^ 36 = 1/2 * 1/2^35 * 1/5^35
{ 1/4 = 1 /2 ^ 2 and using the formula (a^b)^c = a^(b*c) and splitting 1/10 as 1/2 * 1/5 and distributing the exponents using (ab)^m = a ^ m * b ^ m
i.e let a =1/2 b =1/5}
= 1/5 ^ m 1/2 ^ 36 = 1/5^35 * 1/2^36
{1/2 ^ 1 * 1/2 ^ 35 = 1/2 ^ 36
a ^ m * a ^ n = a ^ m+n i.e. a = 1/2 m=1 n =35}
m = 35[/b]
Let me explain
1/5 ^ m 1/4 ^ 18 = 1/2 * 1/10 ^ 35
= 1/5 ^ m 1/2 ^ 36 = 1/2 * 1/2^35 * 1/5^35
{ 1/4 = 1 /2 ^ 2 and using the formula (a^b)^c = a^(b*c) and splitting 1/10 as 1/2 * 1/5 and distributing the exponents using (ab)^m = a ^ m * b ^ m
i.e let a =1/2 b =1/5}
= 1/5 ^ m 1/2 ^ 36 = 1/5^35 * 1/2^36
{1/2 ^ 1 * 1/2 ^ 35 = 1/2 ^ 36
a ^ m * a ^ n = a ^ m+n i.e. a = 1/2 m=1 n =35}
m = 35[/b]
