Question

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.

Answer 1

The correct answer would be C

Answer 2

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.