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

2 Answers
kceylan
Dec 24, 2016

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

smendyka
Dec 24, 2016

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)

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