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

Question

746^25/746^4
Hint: What does the quotient rule of exponents tell us to do if the base is the same?
(1 point)

True
False
Keep the base the same.

Add the exponents to get 29.

Subtract the exponents to get 21.

The final answer is 74621
•

Answer 1

To simplify \( \frac{746^{25}}{746^{4}} \), we can use the quotient rule of exponents. The rule states that when you divide two powers with the same base, you subtract the exponents:

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

In this case:

• The base \( a \) is \( 746 \).
• The exponent \( m \) is \( 25 \).
• The exponent \( n \) is \( 4 \).

Applying the quotient rule:

\[ \frac{746^{25}}{746^{4}} = 746^{25-4} = 746^{21} \]

So, the final answer is:

\[ 746^{21} \]

Thus, the correct answer among your options is:

Subtract the exponents to get 21.

And the final result is:

746^{21}.

Answer 2

It’s a true or false question

Answer 3

Understood! Based on your original message, let’s analyze the statements regarding the quotient rule of exponents:

1. Keep the base the same.

   • False. The rule allows us to simplify the expression by changing the exponent, rather than keeping the base the same.

2. Add the exponents to get 29.

   • False. We subtract the exponents instead of adding them.

3. Subtract the exponents to get 21.

   • True. We correctly subtract \( 25 - 4 \) to get 21.

4. The final answer is 74621.

   • False. The correct form is \( 746^{21} \).

Therefore, the correct true or false statement is:

Subtract the exponents to get 21: True.