Question

When 36x^7y^3/4x^2y^-4 is simplified, the result can be written in the form ax^b y^c, where a is the coefficient, b is the exponent on the variable x, and c is the exponent on the variable y. Find the values of a, b, and c

Answer 1

a = 9 , b = 5 , c = 7

Explanation:

using the rule of exponents

•
`(a^(m) )/(a^(n) )` =
`a^((m-n))`

given

`(36x^7y^3)/(4x^2y^-4)` ← separate the product of the variables

=
`(36)/(4)` ×
`(x^7)/(x^2)` ×
`(y^3)/(y^-4)` ← use the above rule to simplify

= 9 ×
`x^((7-2))` ×
`y^((3-(-4)))`

= 9 ×
`x^(5)` ×
`y^(3+4))`

= 9
`x^(5)`
`y^(7)` ← in the form a
`x^(b)`
`y^(c)`

with a = 9 , b = 5 , c = 7