Question

please look at the picture! answer needed quick, "which expression is NOT equal to the expression shown?"

Answer 1

Exponents

We know that the negative exponents exchange the order of the fraction. For example,

`(1)/(3^(-4))=3^4`

If the exponent 4 was negative down, when it is up it is positive.

Then,

`(3^3)/(3^(-4))=3^3\cdot3^4`

When two exponents with the same base are multiplying their exponents are added, then

`3^3\cdot3^4=3^(3+4)=3^7`

when one is the dividing the other, their exponents are subtracted:

`(3^3)/(3^(-4))=3^(3-(-4))=3^(3+4)=3^7`

In all the options we have 3⁷:

`\begin{gathered} (3^7)/(3^0)=3^(7-0)=3^7 \\ 3^3\cdot3^4=3^(3+4)=3^7 \\ 3\cdot3^6=3^(1+6)=3^7 \end{gathered}`

But, for the first option:

`(3^(-3))/(3^4)=3^(-3-4)=3^(-7)`

Then, the only option that is not equal is the first

Answer: A