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

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

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Answer 1 · 2016-12-24T17:56:20

$8 b^{14} c^{8} d^{6}$ $8b^14c^8d^6$

Explanation:

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

Therefore $(b^{8} c^{6} d^{5}) (8 b^{6} c^{2} d) = 8 b^{14} c^{8} d^{6}$ $(b^8c^6d^5)(8b^6c^2d) = 8b^14c^8d^6$

Answer 2 · 2016-12-24T17:59:27

$8 b^{14} c^{8} d^{6}$ $8b^14c^8d^6$

Explanation:

Step 1) Combine the terms in parenthesis:

$(b^{8} c^{6} d^{5}) (8 b^{6} c^{2} d) \to b^{8} c^{6} d^{5} 8 b^{6} c^{2} d$ $(color(red)(b^8)color(blue)(c^6)color(green)(d^5))(8color(red)(b^6)color(blue)(c^2)color(green)(d)) -> color(red)(b^8)color(blue)(c^6)color(green)(d^5)8color(red)(b^6)color(blue)(c^2)color(green)(d)$

Now we can group like terms:

$b^{8} c^{6} d^{5} 8 b^{6} c^{2} d \to 8 b^{8} b^{6} c^{6} c^{2} d^{5} d$ $color(red)(b^8)color(blue)(c^6)color(green)(d^5)8color(red)(b^6)color(blue)(c^2)color(green)(d) -> 8color(red)(b^8)color(red)(b^6)color(blue)(c^6)color(blue)(c^2)color(green)(d^5)color(green)(d)$

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

$x^{a} x^{b} = x^{a + b}$ $color(purple)(x^ax^b = x^(a+b))$

Using this rule we can now combine like terms:

$8 b^{8} b^{6} c^{6} c^{2} d^{5} d \to 8 b^{8 + 6} c^{6 + 2} d^{5 + 1} \to 8 b^{14} c^{8} d^{6}$ $8color(red)(b^8)color(red)(b^6)color(blue)(c^6)color(blue)(c^2)color(green)(d^5)color(green)(d) -> 8color(red)(b^(8+6))color(blue)(c^(6+2))color(green)(d^(5+1)) -> 8color(red)(b^14)color(blue)(c^8)color(green)(d^6)$

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

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