Question

How do you simplify `(b^8c^6d^5)(8b^6c^2d)`?

Answer 1

`8b^14c^8d^6`

Explanation:

for mulıplication only sum the power of the same terms, i.e:
`b^8*b^6=b^14` then similarly `c^6*c^2=c^8` and `d^5*d= d^6`

Therefore `(b^8c^6d^5)(8b^6c^2d) = 8b^14c^8d^6`

Answer 2

`8b^14c^8d^6`

Explanation:

Step 1) Combine the terms in parenthesis:

`(color(red)(b^8)color(blue)(c^6)color(green)(d^5))(8color(red)(b^6)color(blue)(c^2)color(green)(d)) -> color(red)(b^8)color(blue)(c^6)color(green)(d^5)8color(red)(b^6)color(blue)(c^2)color(green)(d)`

Now we can group like terms:

`color(red)(b^8)color(blue)(c^6)color(green)(d^5)8color(red)(b^6)color(blue)(c^2)color(green)(d) -> 8color(red)(b^8)color(red)(b^6)color(blue)(c^6)color(blue)(c^2)color(green)(d^5)color(green)(d)`

For the next step in the simplification we need to use the following rule for exponents:

`color(purple)(x^ax^b = x^(a+b))`

Using this rule we can now combine like terms:

`8color(red)(b^8)color(red)(b^6)color(blue)(c^6)color(blue)(c^2)color(green)(d^5)color(green)(d) -> 8color(red)(b^(8+6))color(blue)(c^(6+2))color(green)(d^(5+1)) -> 8color(red)(b^14)color(blue)(c^8)color(green)(d^6)`