Question

How do you simplify $ \left( { - 2{u^2}} \right)\left( {6{u^6}} \right) $

Answer 1

Hint: In order to simplify the expression given , combine the exponent values of variable $ u $ by simply adding up their power according to the property of exponents $ {a^m} \times {a^n} = {a^{m + n}} $ ,since the base part is same. Multiply constant values together and rewrite the expression by combining both the results to get the required result.

Complete step-by-step answer:
We are given an expression as $ \left( { - 2{u^2}} \right)\left( {6{u^6}} \right) $ .
As per the question we have to find the product of $ \left( { - 2{u^2}} \right) $ and $ \left( {6{u^6}} \right) $
 $ \Rightarrow \left( { - 2{u^2}} \right)\left( {6{u^6}} \right) $
Rewriting the above expression as
 $ \Rightarrow \left( { - 2 \times 6} \right)\left( {{u^2} \times {u^6}} \right) $
in order to combine the exponent values of variable $ u $ in both the terms, we will using the property of exponent which is $ {a^m} \times {a^n} = {a^{m + n}} $
And for the multiplication of constant part remember the when negative and positive signs multiply , it results into negative sign
 $ \Rightarrow \left( { - 12} \right)\left( {{u^{2 + 6}}} \right) $
Simplifying further, we get
 $
   \Rightarrow \left( { - 12} \right)\left( {{u^8}} \right) \\
   \Rightarrow - 12{u^8} \;
  $
Therefore, the simplification of $ \left( { - 2{u^2}} \right)\left( {6{u^6}} \right) $ is equal to $ - 12{u^8} $ .
So, the correct answer is “ $ - 12{u^8} $ .”.

Note: 1. Multiplication of negative and positive or vice-versa is always negative but when two negatives are multiplied it results in positive.
2.The property of exponents used in the solution is only applicable when the base of the two or more exponent terms is the same.
3. If the exponent terms with the same base are given in division form , you can simply subtract the exponent values.