Use the Product Rule of Exponents to simplify 510⋅55(1 point)
Responses
550
5 superscript 50 baseline
2550
25 superscript 50 baseline
515
5 superscript 15 baseline
2515
The correct answer is 515.
Find the numerical equivalent of 99⋅9−6.(1 point)
Well, the Product Rule of Exponents states that when you have the same base raised to different exponents and you multiply them, you can simply add the exponents together.
So in this case, we have 5 raised to the 10th power multiplied by 5 raised to the 5th power. Adding these exponents together would give us 5 raised to the 15th power.
Therefore, the simplified expression would be 5^15.
To simplify the expression using the Product Rule of Exponents, you can combine the two terms with the same base:
510 * 55 can be written as (5^10) * (5^5).
According to the Product Rule of Exponents, when multiplying two terms with the same base, you add their exponents. Therefore, the expression simplifies to:
5^(10+5) = 5^15.
So, the simplified expression is 5^15.
To simplify the expression 510⋅55 using the Product Rule of Exponents, we need to multiply the base numbers (5 and 5) and add their exponents (10 and 5).
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, you keep the base and add the exponents.
In this case, we have 5^10 ⋅ 5^5.
First, let's multiply the base numbers: 5 ⋅ 5 = 25.
Next, let's add the exponents: 10 + 5 = 15.
Therefore, the simplified expression is 5^15.