Product Rule of Exponents Quick Check
1 of 51 of 5 Items
Question
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
327
32 superscript 7 baseline
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
62⋅73
left parenthesis 6 squared right parenthesis times left parenthesis 7 cubed right parenthesis
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
20015
200 superscript 15 baseline
10,00015
10,000 superscript 15 baseline
10015
100 superscript 15 baseline
10056
guys, dont listen to the bot when it comes to math like this, ive been getting bad grades listening to it
The expression that is correctly developed to use the Product Rule of Exponents is:
(10^8) * (10^8)
To determine which expression correctly uses the Product Rule of Exponents, we need to understand what the Product Rule of Exponents is.
The Product Rule of Exponents states that when multiplying two terms with the same base, you can add their exponents. In other words, if you have x^a * x^b, then it simplifies to x^(a+b).
Now let's analyze the given options:
1) (52)^9: This expression does not involve multiplication, so it does not apply the Product Rule of Exponents. The base is 5, but the exponents are not being added or multiplied.
2) (5^2)^9: This expression involves exponentiation but not multiplication. It simplifies to (25)^9, not using the Product Rule of Exponents either.
3) 10^8 * 10^8: This expression correctly uses the Product Rule of Exponents. Since the base is 10 in both terms, we can add the exponents: 8 + 8 = 16. So the expression simplifies to 10^16.
4) 6^2 * 7^3: This expression involves multiplication but not the same base. Therefore, it does not apply the Product Rule of Exponents.
From the given options, the expression that correctly uses the Product Rule of Exponents is 10^8 * 10^8.