Question

Which sign makes the statement true?
-8 1/5
-8 3/4
(1 point)
>
<
=

Answer 1

Put these numbers in order from least to greatest.
13, 4/5, 0.9, 7/35 ,-13.5
Hint: You can change all the numbers to decimals if they are not already in that form to help you compare.
(1 point)
13
0.9
4/5
7/35
-13.5

Answer 2

Which expression is equivalent to 2 - 26?
Hint: What does the product rule of exponents tell us to do if the base is the same?
(1 point)
2^6
1/2^-7
2^7
2^5

Answer 3

To determine the relation between the two numbers, we first need to convert them into improper fractions or decimals for easier comparison.

-8 1/5 can be converted to a decimal:
-8 1/5 = -8 - 0.2 = -8.2

-8 3/4 can be converted to a decimal:
-8 3/4 = -8 - 0.75 = -8.75

Now we compare -8.2 and -8.75:
-8.2 is greater than -8.75.

Therefore, the correct sign to make the statement true is:

**>**

So, -8 1/5 > -8 3/4.

Answer 4

Let's convert all the numbers to decimals to make it easier to compare them:

1. **13**: This is already in decimal form.
2. **0.9**: This is already in decimal form.
3. **4/5**: To convert this to a decimal, we divide 4 by 5:
\[
4 ÷ 5 = 0.8
\]
4. **7/35**: To convert this to a decimal, we can simplify first:
\[
7 ÷ 35 = 0.2
\]
5. **-13.5**: This is already in decimal form.

Now we have the following decimal values:
- 13
- 0.9
- 0.8 (for 4/5)
- 0.2 (for 7/35)
- -13.5

Now, we can put these numbers in order from least to greatest:
- **-13.5**
- **0.2** (which is 7/35)
- **0.8** (which is 4/5)
- **0.9**
- **13**

Thus, the order from least to greatest is:
**-13.5, 7/35, 4/5, 0.9, 13**.

Answer 5

To simplify the expression \(2 - 26\):

Using the properties of exponents, we can rewrite \(2 - 26\) as:

\[
2^1 - 2^6
\]

Now, using the product rule of exponents, we've established that \(a^m - a^n\) can factor out \(a^{\text{min}(m,n)}\):

\[
2^1 - 2^6 = 2^1(1 - 2^{6-1}) = 2^1(1 - 2^5)
\]

However, that doesn't quite match with your options, so let's analyze the numbers again directly in terms of exponents.

Note:
- \(2^6 = 64\)
- \(2^1 = 2\)

Calculating \(2 - 2^6\):
\[
2 - 64 = -62
\]

We can also interpret \(2 - 26\) as \(2 - 2^6\):

Now, looking at your options:
1. **\(2^6\)** is equal to \(64\).
2. **\(\frac{1}{2^{-7}}\)** simplifies to \(2^7\) (since \(\frac{1}{a^{-b}} = a^b\)).
3. **\(2^7 = 128\)**.
4. **\(2^5 = 32\)**.

None of these expressions simplify directly to \(2 - 26\).

However, if \(2 - 26\) means the difference in exponents. \( 26 = 2^6\), and thus can be interpreted as:

To arrive at equivalent forms:
\(-26 = - (2^6)\) could lead to interpret various comparisons.

If we are aligning exponentials/consolidating logical equivalents, writing the \(2^{-7}\) appears relevant in terms of inverse operations, maintaining relevance on potential similar queries.

So really focusing on the hint, understanding exponent bases and acknowledging \(1/2^{-7}\) could provide an adaptable critical point between alternatives.

Thus I can conclude:
The best representation from the options you listed would be **\(1/2^{-7}\)**.

If meant differently let me know for better evaluations.