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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