Question

Find the value of $ {x^{ - 3}} $ if $ x = {\left( {100} \right)^{1 - 4}} \div {\left( {100} \right)^0} $ ?

Answer 1

Hint: In the given question, we are required to find the value of algebraic expression $ {x^{ - 3}} $ with the help of information given to us. We are given the value of variable x as $ x = {\left( {100} \right)^{1 - 4}} \div {\left( {100} \right)^0} $ . First, we simplify the value of the variable x given to us. Then, we substitute the value of the variable in the expression that we are required to evaluate.

Complete step by step solution:
So, we are given the value of variable x as $ x = {\left( {100} \right)^{1 - 4}} \div {\left( {100} \right)^0} $ .
Firstly, we simplify the value of variable x in order to solve the given problem.
We know that the value of any number raised to the power zero is $ 1 $ . So, we get the value of $ {\left( {100} \right)^0} $ as $ 1 $ . So, substituting the value of $ {\left( {100} \right)^0} $ in the expression, we get the value of x as,
 $ \Rightarrow x = {\left( {100} \right)^{1 - 4}} \div 1 $
Now, we know that when a number is divided by $ 1 $ , we get the result as the number itself. Hence, we get the value of x as,
 $ \Rightarrow x = {\left( {100} \right)^{ - 3}} $
So, we get the value of variable x as $ {\left( {100} \right)^{ - 3}} $ . Now, we substitute the value of x in the expression $ {x^{ - 3}} $ .
So, we get the value of expression $ {x^{ - 3}} $ as,
 $ \Rightarrow {\left( {{{100}^{ - 3}}} \right)^{ - 3}} $
Now, we know the law of exponents $ {\left( {{a^b}} \right)^c} = {a^{bc}} $ . So, the two exponents get multiplied with each other. Hence, we get,
 $ \Rightarrow {100^{\left( { - 3} \right) \times \left( { - 3} \right)}} $
Now, evaluating the product of the exponents, we get,
 $ \Rightarrow {100^9} $
Now, we know that $ 100 $ is a square of $ 10 $ . So, we get,
 $ \Rightarrow {\left( {{{10}^2}} \right)^9} $
Again using the law of exponent $ {\left( {{a^b}} \right)^c} = {a^{bc}} $ , we get,
 $ \Rightarrow {10^{18}} $
Hence, the value of the expression $ {x^{ - 3}} $ if $ x = {\left( {100} \right)^{1 - 4}} \div {\left( {100} \right)^0} $ is $ {10^{18}} $ .
So, the correct answer is “ $ {10^{18}} $ ”.

Note: If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. Transposition rule involves doing the same mathematical thong on both sides of the equation. We must have a grip over the laws of exponents and powers in order to solve such questions. We must take care of calculations and have accuracy in arithmetic so as to be sure of the final answer.