How do you simplify $(-12c^3d^0f^-2)/(6c^5d^-3f^4)$ ?

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Answer 1 · 2017-06-18T16:15:15

See a solution process below:

First, rewrite this expression as:

$(-12/6)(c^3/c^5)(d^0/d^-3)(f^-2/f^4) =>$

$-2(c^3/c^5)(d^0/d^-3)(f^-2/f^4)$

Next, use this rule of exponents to simplify the $d$ term:

$x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))$

$-2(c^3/c^5)(d^color(red)(0)/d^color(blue)(-3))(f^-2/f^4) =>$

$-2(c^3/c^5)(d^(color(red)(0)-color(blue)(-3)))(f^-2/f^4) =>$

$-2(c^3/c^5)(d^(color(red)(0)+color(blue)(3)))(f^-2/f^4) =>$

$-2(c^3/c^5)d^3(f^-2/f^4)$

Now, use this rule of exponents to simplify the $c$ and $f$ terms:

$x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))$

$-2(c^color(red)(3)/c^color(blue)(5))d^3(f^color(red)(-2)/f^color(blue)(4)) =>$

$-2(1/c^(color(blue)(5)-color(red)(3)))d^3(1/f^(color(blue)(4)-color(red)(-2))) =>$

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

$-2(1/c^2)d^3(1/f^6) =>$

$(-2d^3)/(c^2f^6)$

How do you simplify (-12c^3d^0f^-2)/(6c^5d^-3f^4)(-12c^3d^0f^-2)/(6c^5d^-3f^4)?