Question

which expression is equivalent to 2 x 2^6. 2^6 1/2^-7 2^7 2^5

Answer 1

Simplify. Express your answer using positive exponents

10f^8g^9 x 9f^4g^9

Answer 2

Simplify. express your answer as a single term using exponents
746^25/746^4

keep the base the same true or false
add the exponents to get 29 true or false
subtract the exponents to get 21 true or false
the final answer is 746^21 true or false

Answer 3

A calculator displays 4E-6. How do you write this in scientific notation?

Answer 4

the simplified expression for (3m^2n^9p^9)^2 is equivalent to 9m^4n^18p^18 true or false

Answer 5

What is the length of the hypotenuse? if necessary, round to the nearest tenth. Use the pythagorean theorem to solve for c. The altitude is labelled 6.6 m and the base/adjacent is labelled 4.1 m

Answer 6

To simplify the expression \(2 \times 2^6\):

1. Use the property of exponents: \(a^m \times a^n = a^{m+n}\).
2. Here, \(2\) can be written as \(2^1\).

Thus, we have:
\[
2 \times 2^6 = 2^1 \times 2^6 = 2^{1+6} = 2^7
\]

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

Answer 7

To simplify the expression \(10f^8g^9 \times 9f^4g^9\), follow these steps:

1. **Multiply the coefficients (numerical factors)**:
\[
10 \times 9 = 90
\]

2. **Combine the \(f\) terms using the property of exponents**:
\[
f^8 \times f^4 = f^{8+4} = f^{12}
\]

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

4. **Put it all together**:
\[
10f^8g^9 \times 9f^4g^9 = 90f^{12}g^{18}
\]

Thus, the simplified expression is:
\[
\boxed{90f^{12}g^{18}}
\]

Answer 8

To simplify the expression \(\frac{746^{25}}{746^{4}}\), we can use the property of exponents:

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

This means we will subtract the exponents:

1. **Keep the base the same**: True
\[
\text{Base remains } 746
\]

2. **Add the exponents to get 29**: False
\[
25 + 4 = 29 \quad \text{(incorrect operation for division)}
\]

3. **Subtract the exponents to get 21**: True
\[
25 - 4 = 21
\]

4. **The final answer is \(746^{21}\)**: True

Hence, the correct evaluations are:
- Keep the base the same: **True**
- Add the exponents to get 29: **False**
- Subtract the exponents to get 21: **True**
- The final answer is \(746^{21}\): **True**

Thus, the simplified expression is:
\[
\boxed{746^{21}}
\]

Answer 9

The expression \(4E-6\) is already in scientific notation, where \(E\) stands for exponent.

In scientific notation, this can be interpreted as:

\[
4 \times 10^{-6}
\]

So, the number \(4E-6\) is equivalent to \(4 \times 10^{-6}\) in standard scientific notation.

Answer 10

To simplify the expression \((3m^2n^9p^9)^2\), we will use the property of exponents \((a^m)^n = a^{m \cdot n}\) and apply it to each part of the expression.

1. **Square the coefficient (3)**:
\[
3^2 = 9
\]

2. **Square the exponents for \(m\)**:
\[
(m^2)^2 = m^{2 \cdot 2} = m^4
\]

3. **Square the exponents for \(n\)**:
\[
(n^9)^2 = n^{9 \cdot 2} = n^{18}
\]

4. **Square the exponents for \(p\)**:
\[
(p^9)^2 = p^{9 \cdot 2} = p^{18}
\]

Now, putting it all together, we get:
\[
(3m^2n^9p^9)^2 = 9m^4n^{18}p^{18}
\]

Thus, the statement that the simplified expression for \((3m^2n^9p^9)^2\) is equivalent to \(9m^4n^{18}p^{18}\) is **True**.

Answer 11

To find the length of the hypotenuse \(c\) using the Pythagorean theorem, we can use the formula:

\[
c = \sqrt{a^2 + b^2}
\]

where:
- \(a\) is one leg of the right triangle (the altitude in this case),
- \(b\) is the other leg (the base or adjacent side in this case),
- \(c\) is the hypotenuse.

Given:
- Altitude \(a = 6.6\) m,
- Base \(b = 4.1\) m.

Now we can plug in the values:

\[
c = \sqrt{(6.6)^2 + (4.1)^2}
\]

Calculating \(6.6^2\) and \(4.1^2\):

\[
6.6^2 = 43.56
\]
\[
4.1^2 = 16.81
\]

Now add those values together:

\[
c = \sqrt{43.56 + 16.81} = \sqrt{60.37}
\]

Now, calculating the square root:

\[
c \approx 7.77
\]

Rounding to the nearest tenth:

\[
c \approx 7.8 \text{ m}
\]

Thus, the length of the hypotenuse is approximately \( \boxed{7.8} \) m.