# Divide:(i) $6x^3y^2z^2$ by $3x^2yz$(ii) $15m^2n^3$ by $5m^2n^2$(iii) $24a^3b^3$ by $-8ab$

Given:

The given expressions are:

(i) $6x^3y^2z^2$ by $3x^2yz$

(ii) $15m^2n^3$ by $5m^2n^2$

(iii) $24a^3b^3$ by $-8ab$

To do:

We have to divide 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 $6x^3y^2z^2$ by $3x^2yz$.

$6x^3y^2z^2 \div 3x^2yz=\frac{6}{3}x^{3-2}y^{2-1}z^{2-1}$

$6x^3y^2z^2 \div 3x^2yz=2x^{1}y^{1}z^{1}$

$6x^3y^2z^2 \div 3x^2yz=2xyz$

Hence, $6x^3y^2z^2$ divided by $3x^2yz$ is $2xyz$.

(ii) The given expression is $15m^2n^3$ by $5m^2n^2$.

$15m^2n^3 \div 5m^2n^2=\frac{15}{5}m^{2-2}n^{3-2}$

$15m^2n^3 \div 5m^2n^2=3m^{0}n^{1}$

$15m^2n^3 \div 5m^2n^2=3n$

Hence, $15m^2n^3$ divided by $5m^2n^2$ is $3n$.

(iii) The given expression is $24a^3b^3$ by $-8ab$.

$24a^3b^3 \div (-8ab)=\frac{24}{-8}a^{3-1}b^{3-1}$

$24a^3b^3 \div (-8ab)=-3a^{2}b^{2}$

Hence, $24a^3b^3$ divided by $-8ab$ is $-3a^{2}b^{2}$.

Updated on: 13-Apr-2023

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