Question

What is the value of k in the equation?
20^k/ 20^4 = 20^9

Answer 1

k = 13

Explanation:

20^k / 20^4 = 20^9

20^ k = 20^9 * 20^4

this is a math rule

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

this is because the denominators of a are the same

in this question , the bases are 20

in the case of multiplication when the bases are the same , we add the powers

hence we add the powers

= 9 + 4

= 13

hence k = 13

Answer 2

k = 13

Explanation:

20 ^ k / 20^4 = 20^9

knowing the laws of exponents, diving two numbers of the same base with exponents is like subtracting the exponents, so

k^x / k^y

= k ^ (x - y)

apply that knowledge here

20 ^ k / 20 ^ 4 = 20 ^ 9

20 ^ ( k - 4 ) = 20 ^ 9

now the bases have no use here so ignore them, and just calculate the exponents

k - 4 = 9

solve using inverse operations

k - 4 = 9

+4 +4

k = 13