Simplify. Express your answer as a single term using exponents.

Question

746^25/746ª^4
Hint: What does the quotient rule of exponents tell us to do if the base is the same?
True or False
Keep the base the same.
True or False
Add the exponents to get 29.
True or False
Subtract the exponents to get 21.
True of False
The final answer is 74621

Answer 1

To simplify the expression \(\frac{746^{25}}{746^{a^4}}\) using the quotient rule of exponents, we proceed as follows:

The quotient rule states that when dividing two expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator:

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

Applying this to the given expression:

\[ \frac{746^{25}}{746^{a^4}} = 746^{25 - a^4} \]

So, let's evaluate the statements given:

1. Keep the base the same.

   • True. We keep the base (746) the same.

2. Add the exponents to get 29.

   • False. We subtract the exponents, not add them.

3. Subtract the exponents to get 21.

   • False. We subtract \(25 - a^4\). The result would depend on the value of \(a\).

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

   • False. The final answer is \(746^{25 - a^4}\).

In conclusion, the simplified form of the expression is:

\[ 746^{25 - a^4} \]

Answer 2

How do you write 8.459 × 10-5
Hint:
Scientific Notation
Move the decimal point to the left.
4500 → 4.5 × 10 3
Move the decimal point to the right.
0.0677 → 6.77 × 10-2
positive integer
negative integer
(1 point)
• 8,459
84,5900
• .00008459
-8.459

Answer 3

To write \(8.459 \times 10^{-5}\) in standard decimal notation, you need to move the decimal point to the left, according to the negative exponent. The negative exponent tells you how many places to move the decimal point.

In this case, \(10^{-5}\) means you will move the decimal point 5 places to the left.

Starting with \(8.459\):

1. Move the decimal point 5 places to the left.
2. Moving the decimal point:
   • Move 1 place: \(0.8459\)
   • Move 2 places: \(0.08459\)
   • Move 3 places: \(0.008459\)
   • Move 4 places: \(0.0008459\)
   • Move 5 places: \(0.00008459\)

So, \(8.459 \times 10^{-5}\) in standard decimal notation is:

\[ 0.00008459 \]

In Summary:

• 8,459 is the original number before applying scientific notation.
• 84,5900 is not relevant in this context.
• 0.00008459 is the correct answer for \(8.459 \times 10^{-5}\).
• -8.459 is simply the negative of the original number and not a representation in decimal form.

Thus, the correct standard decimal notation for \(8.459 \times 10^{-5}\) is \(\mathbf{0.00008459}\).

Answer 4

A calculator displays 4E-6. How do you write 4E-6 in scientific notation?
____× 10^__
Hint:
Scientific Notation
Move the decimal point to the left.
4500 → 4.5 × 103
Move the decimal point to the right.
0.0677 → 6.77 × 10-2
positive integer
negative integer
(1 point)
4 × 10^6
-6 × 10^4
4 × 10^-6
4 × 10^4

Answer 5

The notation \(4E-6\) is a way of writing \(4 \times 10^{-6}\) in scientific notation, where \(E\) indicates "exponent" and the number following \(E\) is the exponent of 10.

So, the expression \(4E-6\) is equivalent to:

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

Now, let's evaluate the options provided based on this conversion:

1. \(4 \times 10^{6}\) — This is incorrect.
2. \(-6 \times 10^4\) — This is incorrect.
3. \(4 \times 10^{-6}\) — This is correct.
4. \(4 \times 10^{4}\) — This is incorrect.

Final Answer:

So, the correct way to write \(4E-6\) in scientific notation is:

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