Question

Use the quotient property to simplify expressions with higher roots Number 479

Answer 1

`a)d\:b)m`

1) We can simplify those radicals by applying exponents properties.

a) So, let's begin with that:

`a)\sqrt[5]{(d^(12))/(d^7)}\Rightarrow\sqrt[5]{d^(12-7)}\Rightarrow\sqrt[5]{d^5}=d`

b)

`b)\sqrt[8]{(m^(12))/(m^4)}\Rightarrow\sqrt[8]{m^(12-4)}\Rightarrow\sqrt[8]{m^8}\Rightarrow m`

Note that for both cases the exponent is equal to the index of those roots. .