Question

How do you simplify $ - {10^2} $ ?

Answer 1

Hint: We can see this problem is from indices and powers. This number given is having $ 10 $ as base and $ 2 $ as power. We are given a negative power which means that we would first have to take reciprocal of the expression and then continue calculating the value of the expression further. So, then we have to find out the square root of the base number. The result thus obtained will be the answer to the given question.

Complete step-by-step answer:
So, the given question requires us to simplify the value of $ 10 $ raised to the power $ 2 $ first and then multiply the given expression by $ \left( { - 1} \right) $ .
So, we have, $ - {10^2} $
Now, we first square the base. So, we have to calculate the square of $ 10 $ . We know that the square of $ 10 $ is $ 100 $ . So, we get,
 $ \Rightarrow - \left( {100} \right) $
Opening the bracket and representing the answer in a more presentable way, we get,
 $ \Rightarrow - 100 $
So, the value of $ - {10^2} $ can be simplified as $ - 100 $ .
So, the correct answer is “-100”.

Note: These rules or laws of indices help us to minimize the problems and get the answer in very less time. These powers can be positive and negative but can be moulded according to our convenience while solving the problem. Also note that cube-root, square-root is fractions with 1 as numerator and respective root in denominator. We should remember the squares of first $ 20 $ natural numbers so as to do such questions quickly.