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:

$a)\sqrt[5]{\frac{d^{12}}{d^7}}\Rightarrow\sqrt[5]{d^{12-7}}\Rightarrow\sqrt[5]{d^5}=d$

b)

$b)\sqrt[8]{\frac{m^{12}}{m^4}}\Rightarrow\sqrt[8]{m^{12-4}}\Rightarrow\sqrt[8]{m^8}\Rightarrow m$

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