Question

How do you multiply `(3a ^ { 5} b ^ { 3} c ^ { 3} ) ^ { 2} ( 2a ^ { 2} b ^ { 5} c ^ { 4} ) ^ { 3}`?

Answer 1

Multiply and then add the exponents.

Explanation:

We have:

`f=(3a^5b^3c^3)^2(2a^2b^5c^4)^3`

Given that `(a^5)^2=a^(10)` by multiplying exponents we get:

`f=3^2a^(10)b^6c^6 2^3a^6b^(15)c^(12)`

Given that `a^(10)a^6=a^(16)` by adding exponents we get:

`f=72a^(16)b^(21)c^(18)`