Question

Which of the following is a step in simplifying the expression x multiplied by y to the power of 4 over x to the power of negative 5 multiplied by y to the power of 5, the whole to the power of negative 3.?
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

Answer:

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.

Step-by-step explanation:

Given:

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

Now We need to Simplify the given expression;

So by using Law of Indices which states

$(a^m)^n=a^{mn}$

So By applying the same law in above expression we get;

$\frac{x^{-3}y^{4\times-3}}{x^{-5\times-3}y^{5\times-3}}\\\\=\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}$

Hence the correct option from given option 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 15 multiplied by y to the power of negative 15.