Question

Simplify the expression shown below: (a2 b5 c3)4 (a3 b3)3 (a2 c)2.

A) a24 b39 c28
B) a25 b39 c28
C) a26 b42 c31
D) a26 b39 c28

Answer 1

To simplify the given expression, raise each term inside the parentheses to the appropriate exponent and then multiply the terms together. Finally, combine the terms by multiplying the coefficients and adding the exponents of the same variables.

Step-by-step explanation:

To simplify the expression (a2 b5 c3)4 (a3 b3)3 (a2 c)2, we need to raise each term inside the parentheses to the appropriate exponent and then multiply the terms together.

Using the exponent rules, we have (a2 b5 c3)4 = a8 b20 c12, (a3 b3)3 = a9 b9, and (a2 c)2 = a4 c2.

Now we can combine the terms by multiplying the coefficients and adding the exponents of the same variables.

Therefore, the simplified expression is a8+9+4 b20+9 c12+2, which simplifies to a21 b29 c14.