Choose the correct simplification of (a^5b^6)/(a^4b^4) (a) a^9b^1^0 (b) ab^2 (c) (1)/(ab^2) (d) (1)/(a^9b^1^0)

Question

Choose the correct simplification of
`(a^5b^6)/(a^4b^4)`

(a)
`a^9b^1^0`
(b)
`ab^2`
(c)
`(1)/(ab^2)`
(d)
`(1)/(a^9b^1^0)`

Answer 1

a^5 - a^4 = a1 or a

b^6 - b^4 = b2

put them together and you get ab^2

I also took the test and got it right

Answer 2

The correct simplification will be: (b) ab²

`(a^5 b^6)/(a^4 b^4)`

Here we will use the property of exponents for division of two exponential terms with same bases. The original property is :
`(x^m)/(x^n) = x^m^-^n`

It means if the bases are same , then we will just subtract the exponents while dividing two terms.

Using this property:

`(a^5)/(a^4) = a^5^-^4 = a^1 = a`

and
`(b^6)/(b^4) = b^6^-^4 = b^2`

So,
`image`