Question

Which expression is not equal to the expression shown?
(3 ^ 3) / (3 ^ - 4)
3 x 36
33 x 34
(3 ^ - 3) / (3 ^ 4)
(3 ^ 7) / (3 ^ 0)

Answer 1

To determine which expression is not equal to \((3^3) / (3^{-4})\), we can simplify it first.

Using the laws of exponents, we have:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

So we can simplify \((3^3) / (3^{-4})\):

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

Now that we have established that \((3^3) / (3^{-4}) = 3^7\), we can compare this with the provided expressions:

1. **\(3 \times 36\)**:
\[
3 \times 36 = 108 \quad \text{(not equal to \(3^7\))}
\]

2. **\(33 \times 34\)**:
\[
33 \times 34 = 1122 \quad \text{(not equal to \(3^7\))}
\]

3. **\((3^{-3}) / (3^4)\)**:
\[
\frac{3^{-3}}{3^4} = 3^{-3 - 4} = 3^{-7} \quad \text{(not equal to \(3^7\))}
\]

4. **\((3^7) / (3^0)\)**:
\[
\frac{3^7}{3^0} = 3^{7 - 0} = 3^7 \quad \text{(equal to \(3^7\))}
\]

So now we can summarize the results of our checks:

- \(3 \times 36 = 108\)
- \(33 \times 34 = 1122\)
- \((3^{-3}) / (3^4) = 3^{-7}\)
- \((3^7) / (3^0) = 3^7\)

Looking at these results, both \(3 \times 36\) and \(33 \times 34\) are not equal to \(3^7\), as well as \((3^{-3}) / (3^4)\).

The expression that is notably the furthest from equality is \(3 \times 36\) which yields \(108\).

So, the answer is:

**\(3 \times 36\)** is not equal to the original expression \((3^3) / (3^{-4})\).