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,

$\frac{1}{3^{-4}}=3^4$

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

Then,

$\frac{3^3}{3^{-4}}=3^3\cdot3^4$

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:

$\frac{3^3}{3^{-4}}=3^{3-(-4)}=3^{3+4}=3^7$

In all the options we have 3⁷:

$\begin{gathered} \frac{3^7}{3^0}=3^{7-0}=3^7 \\ 3^3\cdot3^4=3^{3+4}=3^7 \\ 3\cdot3^6=3^{1+6}=3^7 \end{gathered}$

But, for the first option:

$\frac{3^{-3}}{3^4}=3^{-3-4}=3^{-7}$

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

Answer: A