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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 $8a^{2}b^{3}c^{5}$.
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