Simplify:
(i) $\frac{16m^3y^2}{4m^2y}$
(ii) $\frac{32m^2n^3p^2}{4mnp}$

Given:

The given expressions are:

(i) $\frac{16m^3y^2}{4m^2y}$

(ii) $\frac{32m^2n^3p^2}{4mnp}$

To do:

We have to simplify the given expressions.

Solution:

We have to divide the given polynomials by monomials using the formula $x^a \div x^b=a^{a-b}$

Polynomials: 

Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.

Monomial:

A monomial is an expression that contains a single term composed of a product of constants and variables with non-negative integer exponents. 

Therefore,

(i) The given expression is $\frac{16m^3y^2}{4m^2y}$

$\frac{16m^3y^2}{4m^2y}=\frac{16}{4}m^{3-2}y^{2-1}$

$\frac{16m^3y^2}{4m^2y}=4m^{1}y^{1}$

$\frac{16m^3y^2}{4m^2y}=4my$

Hence, $\frac{16m^3y^2}{4m^2y}=4my$.

(ii) The given expression is $\frac{32m^2n^3p^2}{4mnp}$.

$\frac{32m^2n^3p^2}{4mnp}=\frac{32}{4}m^{2-1}n^{3-1}p^{2-1}$

$\frac{32m^2n^3p^2}{4mnp}=8m^{1}n^{2}p^{1}$

$\frac{32m^2n^3p^2}{4mnp}=8mn^2p$

Hence, $\frac{32m^2n^3p^2}{4mnp}=8mn^2p$.

Akhileshwar Nani

e

Updated on: 13-Apr-2023

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