Question

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Question 1
Which of the following expressions equal 1? Select ALL that apply. (2 points)
Responses

m0
m to the 0 power

w9
w to the 9th power

890
89 to the 0 power

671
67 to the 1th power
Question 2
Simplify the expression. Write your answer as a fraction. (1 point)
3−4=

Answer 1

### Question 1
To determine which of the following expressions equal 1, we need to recall the rules of exponents:

1. Any non-zero number raised to the power of 0 is equal to 1 (e.g., \(m^0 = 1\)).
2. A number raised to the power of 1 equals the number itself (e.g., \(67^1 = 67\)).
3. The value of an exponent does not influence the outcome of powers of 0.

Now, let's analyze each option.

1. **m0** (or \(m^0\)): This expression equals 1, provided \(m \neq 0\).
2. **w9** (or \(w^9\)): This does not equal 1, as it equals \(w\) multiplied by itself 9 times.
3. **890** (or \(89^0\)): This equals 1, following the rule that any non-zero number raised to the power of 0 equals 1.
4. **671** (or \(67^1\)): This equals 67, as raising to the power of 1 gives the number itself.

Thus, the expressions that equal 1 are:

- **m0** (m to the 0 power)
- **890** (89 to the 0 power)

### Question 2
To simplify the expression \(3^{-4}\), we can use the rule that \(a^{-n} = \frac{1}{a^{n}}\).

Thus:
\[
3^{-4} = \frac{1}{3^{4}} = \frac{1}{81}
\]

So, the simplified answer as a fraction is:

\(\frac{1}{81}\)