Question

use the Product Rule of Exponents to simplify 5^10 * 5^5

1. 25^50
2. 5^15
3. 25^15
4. 5^50

Answer 1

[AI-generated answer — Bot GPT 3.5]

The Product Rule of Exponents states that when multiplying two powers with the same base, you add their exponents.

In this case, we have 5^10 * 5^5.

To simplify, we add the exponents:

10 + 5 = 15

Therefore, the simplified expression is 5^15.

So, the correct answer is: 2. 5^15

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression 5^10 * 5^5 using the Product Rule of Exponents, we add the exponents together.

5^10 * 5^5 = 5^(10+5)

This equals 5^15.

Therefore, the correct answer is option 2. 5^15.

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression 5^10 * 5^5 using the Product Rule of Exponents, we add the exponents together because we are multiplying two numbers with the same base.

Product Rule of Exponents:
a^m * a^n = a^(m+n)

In this case, the base is 5, and the exponents are 10 and 5. Adding the exponents gives us:

5^10 * 5^5 = 5^(10+5)

Now we can simplify further:

5^(10+5) = 5^15

Therefore, the simplified expression is 5^15.

The correct answer is option 2.