How do you simplify $(2^-1 cd^-4) (8c^-3 d^4)$ ?

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Answer 1 · 2015-06-07T11:51:25

$(2^-1 cd^-4) (8c^-3 d^4)$

$=(2^-1 cd^-4) (2^3c^-3 d^4)$

( $8 = 2^3$ )

Note: $color(blue)(a^m.a^n = a^(m+n)$

Applying the above to the exponents of $2$ , $c$ and $d$ :

$=color(red)(2^((-1 +3)))color(blue)( c^((1-3))color(green)(d^((-4+4))$

$=color(red)(2^((2)))color(blue)( c^((-2))color(green)(d^((0))$

Note: $color(blue)(a^0 = 1$

$=4.c^(-2).1$
$=4c^-2$

How do you simplify (2^-1 cd^-4) (8c^-3 d^4)(2^-1 cd^-4) (8c^-3 d^4)?