Question

Which point on the number line shows the position of 8𝜋?

A B C D
<----|-------------|------------|-----------|-------------|------------|---------|----->
25 26 27 28

Hint: What number does 𝜋 equal? Multiply by 8 to see which point it is closest to.


O. A

O. B

O. C

O. D

Answer 1

To find the position of \( 8\pi \) on the number line, we first need to know the approximate value of \( \pi \). The commonly used approximation is:

\[
\pi \approx 3.14
\]

Now, we can calculate \( 8\pi \):

\[
8\pi \approx 8 \times 3.14 = 25.12
\]

Next, we can compare this value to the options given on the number line:

- A: 25
- B: 26
- C: 27
- D: 28

Since \( 25.12 \) is closest to \( 25 \), the point on the number line that shows the position of \( 8\pi \) is:

**O. A**

Answer 2

Which expression is equivalent to 2*2^6?

2^6

1/2^-7

2^7

2^5

Answer 3

To simplify the expression \( 2 \times 2^6 \), we can use the properties of exponents. Specifically, the property states that \( a^m \times a^n = a^{m+n} \).

In this case:

\[
2 \times 2^6 = 2^1 \times 2^6 = 2^{1 + 6} = 2^7
\]

Thus, the expression \( 2 \times 2^6 \) is equivalent to \( 2^7 \).

The correct answer is:

**2^7**

Answer 4

Simplify. Express your answer using positive exponents.

10f^8 g^9*9f^4 g^9

Answer 5

To simplify the expression \(10f^8 g^9 \times 9f^4 g^9\), we will follow the rules of multiplication for coefficients and variables.

1. **Multiply the coefficients**:
\[
10 \times 9 = 90
\]

2. **Combine the like terms for \(f\)** using the property \(a^m \times a^n = a^{m+n}\):
\[
f^8 \times f^4 = f^{8+4} = f^{12}
\]

3. **Combine the like terms for \(g\)**:
\[
g^9 \times g^9 = g^{9+9} = g^{18}
\]

Now, putting it all together, we have:

\[
90f^{12}g^{18}
\]

Thus, the simplified expression is:

\[
\boxed{90f^{12}g^{18}}
\]