# Divide:(i) $-21abc^2$ by $7abc$(ii) $72xyz^2$ by $-9xz$(iii) $-72a^4b^5c^8$ by $-9a^2b^2c^3$

Given:

The given expressions are:

(i) $-21abc^2$ by $7abc$

(ii) $72xyz^2$ by $-9xz$

(iii) $-72a^4b^5c^8$ by $-9a^2b^2c^3$

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 $-21abc^2$ by $7abc$.

$-21abc^2 \div 7abc=\frac{-21}{7}a^{1-1}b^{1-1}c^{2-1}$

$-21abc^2 \div 7abc=-3a^{0}b^{0}c^{1}$

$-21abc^2 \div 7abc=-3c$                    [Since $m^0=1$]

Hence, $-21abc^2$ divided by $7abc$ is $-3c$.

(ii) The given expression is $72xyz^2$ by $-9xz$.

$72xyz^2 \div -9xz=\frac{72}{-9}x^{1-1}yz^{2-1}$

$72xyz^2 \div -9xz=-8x^{0}yz^{1}$

$72xyz^2 \div -9xz=-8yz$                       [Since $m^0=1$]

Hence, $72xyz^2$ divided by $-9xz$ is $-8yz$.

(iii) The given expression is $-72a^4b^5c^8$ by $-9a^2b^2c^3$.

$-72a^4b^5c^8 \div (-9a^2b^2c^3)=\frac{-72}{-9}a^{4-2}b^{5-2}c^{8-3}$

$-72a^4b^5c^8 \div (-9a^2b^2c^3)=8a^{2}b^{3}c^{5}$

Hence, $-72a^4b^5c^8$ divided by $-9a^2b^2c^3$ is $8a^{2}b^{3}c^{5}$.

Updated on: 13-Apr-2023

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