What is the quotient of 2^4/2^-4

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]