How do you simplify ${{\left( {{b}^{3}} \right)}^{5}}$ ?

Hint: In this question, we have to simplify an algebraic expression. Thus, we will use the exponent formula and the basic mathematical rules to get the solution. First, we will open the brackets of the given problem by using the exponent rule, which states that when we have a power of a power rule, then their powers are multiplied to each other, that is ${{\left( {{a}^{b}} \right)}^{c}}={{a}^{bc}}$ . Thus, after the necessary calculations, we get the required solution for the problem.

Complete step by step solution:
According to the question, we have to simplify the given algebraic expression.
Thus, we will apply the exponent rule and the basic mathematical rules to get the solution.
The algebraic expression given to us is ${{\left( {{b}^{3}} \right)}^{5}}$ ----------- (1)
So, we start solving our problem by using the exponent rule which states that when we have a power of a power rule, then the powers are multiplied to each other, that is ${{\left( {{a}^{b}} \right)}^{c}}={{a}^{bc}}$ . Therefore, we will apply this formula in the equation (1), we get
${{\left( b \right)}^{3\times 5}}$
On further solving the above algebraic expression, we get
${{\left( b \right)}^{15}}$
Thus, we cannot simplify the above equation furthermore.

Therefore, for the algebraic equation ${{\left( {{b}^{3}} \right)}^{5}}$ , its simplified value is ${{b}^{15}}$ which is the required solution.

Note: While solving this question, do mention all the steps and the rules properly to avoid mathematical errors. Also, do not forget that the powers are multiplied to each other instead of they are adding to each other.