Question

Find the product:
A. $ {a^2}(2{a^{22)}}(4{a^{26}}) $
B. $ (2/3xy)( - 9/10{x^2}{y^2}) $
C. $ ( - 10/3p{q^3})(6/5{p^3}q) $

Answer 1

Hint: While answering such questions, the like terms are multiplied together i.e. constants with constants and variables with variables and finally the product is written together.

Complete step-by-step answer:
A. $ {a^2}(2{a^{22)}}(4{a^{26}}) $
Separating constants and variables, we get:
 $ $ $ = 2 \times 4 \times {a^2}{a^{22}}{a^{26}} $
 $ = 8 \times {a^{2 + 22 + 26}} $ (power of like terms are added in multiplication)
 $ = 8{a^{50}} $
Therefore, the product obtained is 8a50.

B. $ (2/3xy)( - 9/10{x^2}{y^2}) $
Separating constants and variables, we get:
                   $ = (2/3)\left( { - 9/10)xy \times {x^2}{y^2}} \right) $
                    $ = - 18/30 \times {x^{2 + 1}}{y^{2 + 1}} $
                     $ = - 18/30{x^3}{y^3} $
Therefore, the product obtained $ = - 18/30{x^3}{y^3} $

C. \[x \times {x^2}x \times {x^3} \times {x^4}\]
Here all the terms are like (as x variable)
Thus all the powers will be added on x.
 $ = {x^{1 + 2 + 1 + 3 + 4}} $
 $ = {x^{11}} $
Therefore, the product obtained is $ {x^{11}} $

Note: Powers of like terms are always added when they are multiplied.
Try enclosing negative terms brackets for better clarification while solving the questions.