Question

Evaluate the followings:
A. \[{\left( {1.2} \right)^3}\]
B. \[{\left( {3.5} \right)^3}\]
C. \[{\left( {0.8} \right)^3}\]
D. \[{\left( {0.5} \right)^3}\]

Answer 1

Hint: We will solve this question by writing the power into multiplication form, for example, \[{\left( a \right)^3}\] can be written as \[a \times a \times a\].

Complete step-by-step solution:
Step 1: We will write the term
\[{\left( {1.2} \right)^3}\] into multiplication form as shown below:
\[{\left( {1.2} \right)^3} = 1.2 \times 1.2 \times 1.2\]
By replacing the term
\[1.2 = \dfrac{{12}}{{10}}\] in the above expression we get:
\[ \Rightarrow {\left( {1.2} \right)^3} = \dfrac{{12}}{{10}} \times \dfrac{{12}}{{10}} \times \dfrac{{12}}{{10}}\]
Now by multiplying the numerators and denominators in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {1.2} \right)^3} = \dfrac{{1728}}{{1000}}\]
Now as we know
\[\dfrac{1}{{1000}} = 0.001\] so by applying this in the LHS side of the above expression we get:

\[ \Rightarrow {\left( {1.2} \right)^3} = 1.728\]
Step 2: We will write the term \[{\left( {3.5} \right)^3}\] into multiplication form as shown below:
\[{\left( {3.5} \right)^3} = 3.5 \times 3.5 \times 3.5\]
By replacing the term \[3.5 = \dfrac{{35}}{{10}}\] in the above expression we get:
\[ \Rightarrow {\left( {3.5} \right)^3} = \dfrac{{35}}{{10}} \times \dfrac{{35}}{{10}} \times \dfrac{{35}}{{10}}\]
Now by multiplying the numerators and denominators in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {3.5} \right)^3} = \dfrac{{42875}}{{1000}}\]
Now as we know \[\dfrac{1}{{1000}} = 0.001\] so by applying this in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {3.5} \right)^3} = 42.875\]
Step 3: We will write the term
\[{\left( {0.8} \right)^3}\] into multiplication form as shown below:
\[{\left( {0.8} \right)^3} = 0.8 \times 0.8 \times 0.8\]
By replacing the term \[0.8 = \dfrac{8}{{10}}\] in the above expression we get:
\[ \Rightarrow {\left( {0.8} \right)^3} = \dfrac{8}{{10}} \times \dfrac{8}{{10}} \times \dfrac{8}{{10}}\]
Now by multiplying the numerators and denominators in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {0.8} \right)^3} = \dfrac{{512}}{{1000}}\]
Now as we know
\[\dfrac{1}{{1000}} = 0.001\] so by applying this in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {0.8} \right)^3} = 0.512\]
Step 4: We will write the term
\[{\left( {0.5} \right)^3}\] into multiplication form as shown below:
\[{\left( {0.5} \right)^3} = 0.5 \times 0.5 \times 0.5\]
By replacing the term
\[0.5 = \dfrac{5}{{10}}\] in the above expression we get:
\[ \Rightarrow {\left( {0.5} \right)^3} = \dfrac{5}{{10}} \times \dfrac{5}{{10}} \times \dfrac{5}{{10}}\]
Now by multiplying the numerators and denominators in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {0.5} \right)^3} = \dfrac{{125}}{{1000}}\]
Now as we know \[\dfrac{1}{{1000}} = 0.001\] so by applying this in the LHS side of the above expression we get:
\[ \Rightarrow {\left( {0.5} \right)^3} = 0.125\]

\[{\left( {1.2} \right)^3} = 1.728\], \[{\left( {3.5} \right)^3} = 42.875\],
\[{\left( {0.8} \right)^3} = 0.512\] and \[{\left( {0.5} \right)^3} = 0.125\]

Note: Students need to take care while putting the decimal sign at the end. You should know that if there is one zero in the denominator then the decimal will come before one figure if there are two zeroes then the decimal will come before two figures similarly it will be applied for three zeroes as well. For example:
\[ \Rightarrow \left( {\dfrac{1}{{10}}} \right) = 0.1\]
\[ \Rightarrow \left( {\dfrac{1}{{100}}} \right) = 0.01\]
\[ \Rightarrow \left( {\dfrac{1}{{1000}}} \right) = 0.001\]