How do you simplify #(c ^ { - 14} d ^ { 12} g ^ { - 19} ) ^ { - 20}#?

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Answer 1 · 2017-09-07T23:57:43

See a solution process below:

First, use this rule of exponents to eliminate the outer exponent:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(c^color(red)(-14)d^color(red)(12)g^color(red)(-19))^color(blue)(-20) =>#

#c^(color(red)(-14) xx color(blue)(-20))d^(color(red)(12) xx color(blue)(-20))g^(color(red)(-19) xx color(blue)(-20)) =>#

#c^280d^-240g^380#

Now, use this rule of exponents to eliminate the negative exponent:

#x^color(red)(a) = 1/x^color(red)(-a)#

#c^280d^color(red)(-240)g^380 =>#

#(c^280g^380)/d^color(red)(- -240) =>#

#(c^280g^380)/d^240#