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

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

(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.

Solution:

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

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

 =

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.

Volume of cylinder(V) is given by:

           ....[1]

where, r is the radius of the cylinder and h is the height of the cylinder

From the diagram:

Diameter of a pipe (d) = 10 cm

height of the pipe(h) = 2m    

Use conversion:

1 m = 100 cm

then

2m  = 200 cm

⇒h = 200 cm

Since, a pipe is in the form of cylinder.

We have to find the volume of a pipe.

We know that:

⇒

Divide both sides by 2 we get;

5 = r

or

r = 5 cm

Substitute the given values and use  π = 3.14. in [1] we have;

Simplify:

Therefore, the volume of a pipe in cm³ is, 15700