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