Question

Expanded form of ${{(xy)}^{4}}$ is –
A. (-xy) × (-xy) × (-xy) × (-xy)
B. 4 × (-xy)
C. (-xy) × (-xy)
D. (-xy) × (-xy) × (-xy)

Answer 1

Hint: There are various rules that are applied on numbers and their powers to find the values in an easier way.
The numbers and their powers are connected by four arithmetic operations – addition, subtraction, multiplication and division.

Complete step by step answer:
The rules on base and power of numbers are as follows:
a^m × aⁿ = (a)^{m + n}
a^m ÷ aⁿ = (a)^{m - n}
(ab)^m = a^m × b^m
a^m × b^m = (ab)^m
${{a}^{0}}=1$
The base “a” and “b” can be a whole number or a rational number and the same applies to power also.
Similarly, bases and powers can be negative or positive. This indicates that both bases and powers belong to rational numbers as rational numbers include all types of integers, zero and both positive and negative fractions.
The rules related to base and powers help in calculating complex problems in very less time.
To expand ${{(xy)}^{4}}$, the expression (xy) has to be multiplied by itself as many times as is the power of (xy).
As power of (xy) is $4$, the expanded form is given as:
 $xy\times xy\times xy\times xy$ .
Out of given four options, option A is similar to the correct answer as minus sign when multiplied four times becomes a positive sign as ${{(-1)}^{4}}$ is equal to $+1$. This indicates that option A is correct.
So, the correct answer is “Option A”.

Note: The power of a number denotes the number of times that number has to be multiplied with itself.
For instance, ${{\left( 2 \right)}^{3}}$ denotes that the number $2$ must be multiplied $3$ times to get an answer equal to $2\times 2\times 2$ equal to $8$.