Question

How do you simplify $ {(6{x^2})^4}? $

Answer 1

Hint: We know that the above given question is in exponential form. 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, in the given question $ (6{x^2}) $ is the base and the number $ 4 $ is the exponential power. We can solve the given expression by the product rule. As we know that as per the property of exponent rule if there is $ {(ab)^m} $ then it can be written as $ {a^m} \times {b^m} $ . When we express a number in exponential form then we can say that it’s power has been raised by the exponent.

Complete step-by-step answer:
There is one basic exponential rule that is commonly used everywhere, $ {({a^m})^n} = {a^{m \cdot n}} $ . Also there is another rule and according to the exponent product rule when multiplying two powers that have the same base, we can add the exponents. We can see that in this question $ 6{x^2} $ has $ {6^1}{x^2} $ .
So here we can write the given expression as
$ {(6{x^2})^4} = {6^{^{1 \times 4}}} \times {x^{2 \times 4}} $ . It gives us the value $ {6^4}{x^8} $ .
Hence the required answer of the exponential form is $ {6^4}{x^8} $ .
So, the correct answer is “ $ {6^4}{x^8} $ ”.

Note: We know that exponential equations are equations in which variables occur as exponents. The formula applied before 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 know that the most commonly used exponential function base is the transcendental number which is denoted by $ e $ .