Question

If \[x = 10\], Evaluate \[\dfrac{1}{{50}} \times {x^3}\]

Answer 1

Hint: If the given number is raised to some power (let it be ‘n’) then that number will get multiplied ‘n’ number of times with itself. For example \[{2^4} = 2 \times 2 \times 2 \times 2 = 16\]
Given: \[x = 10\]
To find: the value of \[\dfrac{1}{{50}} \times {x^3}\]

Complete step by step answer:
Step 1: we have an equation\[\dfrac{1}{{50}} \times {x^3}\], now firstly determining the value of x3
As we know, if the given number is raised to some power (let it be ‘n’) then that number will get multiplied ‘n’ number of times with itself.
Here we have \[{x^3}\] so x will get multiplied three times with itself i.e.
\[{x^3} = x \times x \times x\]
Now it is provided in the question that the value of x is equal to 10, therefore substituting the value of x, we get
\[{x^3} = x \times x \times x = 10 \times 10 \times 10\]
Multiplying 10 three times with itself, we get
\[{x^3} = 1000\]
Step 2: Now, we have the equation \[\dfrac{1}{{50}} \times {x^3}\] which means that we have to multiply \[\dfrac{1}{{50}}\] with \[{x^3}\]
Now as we know that if we multiply or divide any number with 1 then we get the same number. Therefore, \[\dfrac{1}{{50}} \times {x^3}\] can also be written as \[\dfrac{1}{{50}} \times \dfrac{{{x^3}}}{1}\]
Multiplying numerator with numerator and denominator with denominator, we get
\[\dfrac{1}{{50}} \times \dfrac{{{x^3}}}{1} = \dfrac{{1 \times {x^3}}}{{50 \times 1}} = \dfrac{{{x^3}}}{{50}}\]
Step 3: substituting the value of x in\[\dfrac{{{x^3}}}{{50}}\] , we get
\[\dfrac{{{x^3}}}{{50}} = \dfrac{{10 \times 10 \times 10}}{{50}} = \dfrac{{1000}}{{50}}\]
Now dividing 1000 by 50, we get
\[\dfrac{1}{{50}} \times \dfrac{{{x^3}}}{1} = \dfrac{{1000}}{{50}}\]
\[\dfrac{1}{{50}} \times \dfrac{{{x^3}}}{1} = 20\]
Hence, the value \[\dfrac{1}{{50}} \times {x^3}\] is equal to 20.

Note: If the given number is raised to some power (let it be ‘n’) then that number will get multiplied ‘n’ number of times with itself. For example \[{2^4} = 2 \times 2 \times 2 \times 2 = 16\]
If the given number is in the fractional form then multiply numerators of the fractions to get the new numerator and multiply the denominators of the fraction to get a new denominator.