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How do you write \[{{\left( 5n \right)}^{2}}\] without exponents?

Last updated date: 01st Mar 2024
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IVSAT 2024
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Hint: These types of problems are pretty straight forward and are very easy to solve. For such problems we first of all need to understand the meaning of representation without exponents. It simply means that we have to rewrite the given sum in such a way that there are no power present in the final result. In such an operation, if we have any real numbers present, then we need to evaluate it to the resultant power that is given. In case there is any parameter present, we need to write it down in the multiplied form in a linear manner.

Complete step by step answer:
Now we start off with the solution of the given problem by writing that,
In our given problem we have a real number which is basically \[5\] , and we have a power in the problem as \[2\] . So evaluating the power if the real number we get,
\[{{\left( 5 \right)}^{2}}=25\]
Now, we can simplify the problem further as,
\[25{{\left( n \right)}^{2}}\]
We now write the parameter and its power as a linear form of multiplication. Since the power given here is \[2\] , so we need to multiply the parameter two times. On performing this operation to our problem, we get,
\[{{\left( n \right)}^{2}}=n\cdot n\]
Now, on combining both the theories that we have got, we finally can write,
\[{{\left( 5n \right)}^{2}}=25n\cdot n\]

Note: For problems like these, we first need to understand the very core meaning of the problem clearly. Writing the given problem in the form of something which doesn’t involve any power terms, is known as representing it without exponents. We need to be very careful about what the power is and how many times we need to multiply the parameter in order for a proper representation of the given sum.
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