Question

How do you simplify \[{{\left( {{b}^{5}} \right)}^{4}}\]?

Answer 1

Hint: From the question given, we have been asked to simplify \[{{\left( {{b}^{5}} \right)}^{4}}\]. We can simplify the above given exponential expression from the question given by knowing some basic formulae of exponents. By knowing some basic formula of exponents, we can simplify the given expression from the question very easily.

Complete step by step answer:
From the question we had been given that \[{{\left( {{b}^{5}} \right)}^{4}}\]
We can clearly observe that the given expression is in exponential form.
So, we have to know all the basic formulae of the exponents clearly to simplify the given question.
We can clearly observe that the given expression is in the form of \[{{\left( {{x}^{m}} \right)}^{n}}\].
From one of the basic laws of exponents, we have one formula \[{{\left( {{x}^{m}} \right)}^{n}}={{x}^{mn}}\]
By using the above one of the basic laws of exponents, we can simplify the given expression very easily.
By applying the above formula from basic laws of exponents, we get \[{{\left( {{b}^{5}} \right)}^{4}}={{b}^{5\times 4}}\]
On furthermore simplifying the above equation we get \[{{\left( {{b}^{5}} \right)}^{4}}={{b}^{20}}\]
So, as we have already discussed above, we got the simplification by using some basic formula from the basic laws of exponents.
Hence, the given expression is simplified.

Note:
 We should be well aware of the formulae and basic laws of exponents. We should know where the formula is to be used in the given question. If we clearly observe the question, the question can be solved by using one simple formula. So, we should be well aware of the usage of the formulae and basic laws of exponents. There are many other logarithm formulae that help us in answering questions of this type like ${{\log }_{a}}{{a}^{x}}=x$ and ${{\log }_{a}}1=0$ etc….