5^21*4^11=2*10^n
5^21*(2^2)^11=2*(10)^(n)
5^21*2^21=10^n
(10)^21=10^n
n=21
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exponents, no matching bases
Source: Beat The GMAT — Problem Solving |
The basic rule here is that when you calculate the x-root of a base, you then multiply the exponent by x.
For example:
8^2 = 2^6 = 64
Here, you can see that 2 is the cube root of 8. Since a number cubed is a number raised to the 3rd power, you multiply the old exponent (2) from the old base (8) by 3.
9^3 = 3^6 = 729
16^2 = 4^4
For example:
8^2 = 2^6 = 64
Here, you can see that 2 is the cube root of 8. Since a number cubed is a number raised to the 3rd power, you multiply the old exponent (2) from the old base (8) by 3.
9^3 = 3^6 = 729
16^2 = 4^4
