Question

Which of the following expresses zero law of exponents?
A. $ {0^x} = 0 $
B. $ {x^0} = 1 $
C. $ {x^1} = x $
D.None of the above

Answer 1

Hint: We know that an exponent refers to the number of times a number is multiplied by itself. There is base and exponent or power in this type of equation. Here we have to find the correct option which satisfies the zero law of exponents. The zero law of exponent says that any number or expression that is raised to the power of zero is always equal to $ 1 $ .

Complete step-by-step answer:
We know that the law of exponents is mainly based on the exponent part. Therefore the laws are also known as the laws of exponents.
So according to the zero law of exponents, it says that any non- zero number which is raised to the power of zero is equal to $ 1 $ .
We can write the above in expression i.e.
 $ {a^0} = 1 $ , where $ a \ne 0 $ .
So by comparing this from the above given options we can see that the correct format is
 $ {x^0} = 1 $ .
Hence the correct option is (b) $ {x^0} = 1 $ .
So, the correct answer is “Option B”.

Note: We know that exponential equations are equations in which variables occur as exponents. The formula applied is true for all real values of $ m $ and $ n $ . We should solve this kind of problem by using the properties of exponents to simplify the problem. We have to keep in mind that if there is a negative value in the power or exponent then it will reverse the number .i.e.
 $ {m^{ - x}} $ will always be equal to $ \dfrac{1}{{{m^x}}} $ .
We should also know that the most commonly used exponential function base is the transcendental number which is denoted by $ e $ .
 Another property of exponent rule if there is $ \dfrac{{{a^m}}}{{{a^n}}} $ then it can be written as
  $ {a^{m - n}} $ .
We should another exponent rule if there is $ {(ab)^m} $ then it can be written as
 $ {a^m} \times {b^m} $
There is one basic exponential rule that is commonly used everywhere,
  $ {({a^m})^n} = {a^{m \cdot n}} $ .