Evaluate 14412-1/312^3

Problem

144⋅12−1/3⋅12^3

Solution

1. Identify the components of the expression, noting that 144 is equivalent to 12^2

2. Rewrite the first term using powers of 12 to simplify the calculation.

144⋅12=12^2⋅12=12^3

3. Substitute this back into the original expression.

12^3−1/3⋅12^3

4. Factor out the common term 12^3 from the expression.

(1−1/3)⋅12^3

5. Simplify the coefficient inside the parentheses.

2/3⋅12^3

6. Calculate the value of 12^3

12^3=1728

7. Multiply the result by the fraction.

2/3⋅1728=2⋅576=1152

Final Answer

144⋅12−1/3⋅12^3=1152

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