Respuesta :
The expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex] or 3[tex]x^{4-16}[/tex].that is option C) is correct.
According to the question the expression that we have been given to us is :
[tex]\frac{12x^{4} }{4x^{16} }[/tex]
Note that we know the property of exponent which states that if teh exponents with same base and different power are divided then the powers are subtracted. That is,
[tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex] (1)
Now using this rule we will evaluate the equation given that is
= [tex]\frac{12}{4} * \frac{x^{4} }{x^{16} } \\\\[/tex]
First we will divide 12/4 which gives 3 then we will apply the property of exponent to the exponent function which gives,
= 3 [tex]x^{4-16}[/tex]
= 3 [tex]x^{-12}[/tex]
Hence the expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex]or 3[tex]x^{4-16}[/tex] that is option C) is correct.
Learn more about exponent here : https://brainly.com/question/11975096
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