Question

What is not equal to 3^3 divided by 3^-4

Answer 1

Is it 3x3^6, 3^3x3^4, 3^-3divided by3^4, or3^7 divided by 3^0

Answer 2

To simplify the expression \( \frac{3^3}{3^{-4}} \), we can use the properties of exponents. Specifically, the property that states \( \frac{a^m}{a^n} = a^{m-n} \).

So, applying this property:

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

Now, \( 3^7 \) can be computed as:

\[
3^7 = 2187
\]

Thus, \( \frac{3^3}{3^{-4}} \) equals 2187.

Now, to find values that are **not equal** to \( 3^3 \div 3^{-4} \) (which we found to be 2187), any number other than 2187 would suffice. For example, \( 0 \), \( 1 \), \( 2186 \), \( 2188 \), or any other number not equal to \( 2187 \).

In conclusion, 2187 is not equal to itself, and any other number can be considered as not equal to \( \frac{3^3}{3^{-4}} \).

Answer 3

Let's evaluate each of the provided expressions to determine whether they are equal to \( \frac{3^3}{3^{-4}} \), which we already calculated to be \( 3^7 \) or 2187.

1. **Expression: \( 3 \times 3^6 \)**

\[
3 \times 3^6 = 3^1 \times 3^6 = 3^{1+6} = 3^7
\]

2. **Expression: \( 3^3 \times 3^4 \)**

\[
3^3 \times 3^4 = 3^{3+4} = 3^7
\]

3. **Expression: \( \frac{3^{-3}}{3^4} \)**

Using the property \( \frac{a^m}{a^n} = a^{m-n} \):

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

4. **Expression: \( \frac{3^7}{3^0} \)**

Since \( 3^0 = 1 \):

\[
\frac{3^7}{3^0} = \frac{3^7}{1} = 3^7
\]

Now let's summarize the results:

- \( 3 \times 3^6 = 3^7 \)
- \( 3^3 \times 3^4 = 3^7 \)
- \( \frac{3^{-3}}{3^4} = 3^{-7} \) (which is **not** equal to \( 3^7 \))
- \( \frac{3^7}{3^0} = 3^7 \)

Thus, the expression that is **not equal** to \( \frac{3^3}{3^{-4}} \) (or \( 3^7 \)) is \( \frac{3^{-3}}{3^4} \).