Answered

Which of the following is a step in simplifying the expression-


(xy to the power of 4) to the power of -3

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(x to the power -5 y to the power 5) to the power of ?


A-x to the power of negative 3 multiplied by y, the whole over x to the power of negative 8 multiplied by y to the power of 2.


B-x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of negative 5 multiplied by y to the power of 5.


C-x to the power of negative 3 multiplied by y, the whole over x to the power of negative 5 multiplied by y to the power of 5.


D-x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of 15 multiplied by y to the power of negative 15.

Verified Answer :

Sampras

The correct answer would be C

Solution:

The Expression containing variables raised to power i.e Radicals means combination of base and Exponent is

\(\frac{(x y^{4})^{-3}}{(x^{-5} y^{5})^{?}}\)

As while solving these kind of problems, keep in mind the following radical rules:

\(1. (a^m)^{n}=a^{mn}\\\\2.(ab)^{m}=a^mb^n\\\\3.(a^{m})^{-n}=a^{-mn}\)

\(\frac{(x y^{4})^{-3}}{(x^{-5} y^{5})^{?}}\)

 = \(\frac{x^{-3}y^{-12}}{(x^{-5}y^{5})^{?}}\)

So, the first step is in simplifying the expression is Option  B which is →→x to the power of negative 3 multiplied by y to the power of negative 12, the whole over x to the power of negative 5 multiplied by y to the power of 5.

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