Question

Solve $ - 20{x^4} \div 10{x^2} $

Answer 1

Hint: First of all frame the given equation in its equivalent fraction form. And then remove common factors from the numerator and the denominators and then simplify for the resultant required value.

Complete step-by-step answer:
Take the given expression: $ - 20{x^4} \div 10{x^2} $
Frame the above expression in its equivalent form: $ \dfrac{{ - 20{x^4}}}{{10{x^2}}} $
Find the factors for the constant term in the numerator and the denominator.
 $ = - \dfrac{{2 \times 10{x^4}}}{{10{x^2}}} $
Common multiples from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
 $ = - \dfrac{{2{x^4}}}{{{x^2}}} $
Now, use the inverse exponent rule in the above expression where the term if moved to the numerator from the denominator then there is changed in the sign of its power which is expressed as $ {x^{ - n}} = \dfrac{1}{{{x^n}}} $
 $ = - 2{x^4}.{x^{ - 2}} $
Now, by using the law of power and exponent which states that when bases are the same and the terms are in the multiplication then the powers are combined.
 $ = - 2{x^{4 - 2}} $
Simplify the above expression finding the difference of the powers.
 $ = - 2{x^2} $
Hence, the required solution is $ - 20{x^4} \div 10{x^2} = - 2{x^2} $
So, the correct answer is “ $ - 2{x^2} $ ”.

Note: Power and exponent is used to express the mathematical term in short form for example: $ 5 \times 5 \times 5 \times 5 $ is expressed as $ {5^4} $ Also, when you use the inverse exponent rule be careful about the sign convention.