Question

Which expression is equal to 5y^3÷5y^-2

Answer 1

`5y^3/5y^-2` =
`y^5`

Explanation:

`5y^3/5y^-2`

as 5 is both in numerator and denominator it will get cancelled so we have now expression

`y^3/y^-2`

we will use law of indices wherein if there is

`a^x/a^y = a^(x-y)`

which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept

here power in numerator is 3 and power in denominator is -2

hence we will be subtracting -2 from 3

`y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5`

Thus,

`5y^3/5y^-2` =
`y^5`