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

`((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)`

`((x y^(4))^(-3))/((x^(-5) y^(5))^(?))`

=
`(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.