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ANSWER

The quotient is
[tex]256[/tex]

EXPLANATION

The given expression is
[tex] \frac{ {2}^{4} }{ {2}^{ - 4} } [/tex]


This is the same as

[tex] {2}^{4} \times \frac{ 1 }{ {2}^{ - 4} } [/tex]

We apply the property of exponents given below to rewrite the given expression so that it will have only positive indices.


The property is


[tex] \frac{1}{ {a}^{ - m} } = {a}^{m} [/tex]

When we apply this property we obtain,


[tex] = {2}^{4} \times {2}^{4}[/tex]

This simplifies to

[tex] = 16 \times 16[/tex]

This gives us,

[tex] = 256[/tex]

Answer:

Quotient = 256.

Step-by-step explanation:

Given : [tex]\frac{2^{4} }{2^{-4} }[/tex]

To find : What is the quotient.

Solution : We have given that  [tex]\frac{2^{4} }{2^{-4} }[/tex]

By exponent rule 1 :  [tex]\frac{1}{x^{-m} }[/tex] = [tex]x^{m}[/tex]

[tex]\frac{1}{2^{-4} }[/tex] = [tex]2^{4}[/tex]

Then,  = [tex]2^{4}[/tex] * [tex]2^{4}[/tex]    

On simplification [tex]2^{4}[/tex] = 16

Then 16 *16  = 256

Therefore, Quotient = 256.

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