Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
32^7
(5^2)^9
10^8⋅10^8
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is 10^8⋅10^8.
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
100^15
100^56
10,000^15
200^15
The correct response is 10,000^15.
Find the numerical equivalent of 10^2 ⋅10^3
To find the numerical equivalent of 10^2 ⋅10^3, we can use the Product Rule of Exponents, which states that when multiplying two numbers with the same base, you can add their exponents.
In this case, both exponents are positive integers, so we can add them:
10^2 ⋅10^3 = 10^(2+3) = 10^5
Therefore, the numerical equivalent of 10^2 ⋅10^3 is 10^5 = 100,000.
Find the numerical equivalent of 2^5 ⋅2^−2
To find the numerical equivalent of 2^5 ⋅2^−2, we can use the Product Rule of Exponents, which states that when multiplying two numbers with the same base, you can add their exponents.
In this case, we have 2^5 ⋅2^−2. Adding their exponents, we get:
2^(5+(-2)) = 2^3
So the numerical equivalent of 2^5 ⋅2^−2 is 2^3, which is equal to 8.
Find the numerical equivalent of 4^9⋅4^−7
To find the numerical equivalent of 4^9⋅4^−7, we can use the Product Rule of Exponents, which states that when multiplying two numbers with the same base, you can add their exponents.
In this case, we have 4^9 ⋅4^−7. Adding their exponents, we get:
4^(9 + (-7)) = 4^2
So the numerical equivalent of 4^9 ⋅4^−7 is 4^2, which is equal to 16.
In order to determine which expression correctly uses the Product Rule of Exponents, let's first understand what the Product Rule of Exponents states.
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, you can add their exponents. In other words, for any positive integers m and n, and any base number b:
b^m * b^n = b^(m + n)
Now, let's analyze each expression to see which one applies the Product Rule correctly:
1. 32^7: This expression does not involve multiplying two exponential expressions with the same base. It is only raising 32 to the power of 7. Therefore, it does not utilize the Product Rule of Exponents.
2. (5^2)^9: This expression involves raising 5 to the power of 2, and then raising the result to the power of 9. The Product Rule is not relevant here since we don't have multiplication involved.
3. 10^8 * 10^8: This expression properly applies the Product Rule of Exponents. Both exponential expressions have the same base of 10. By applying the Product Rule, we can add the exponents: 10^(8+8) = 10^16.
4. 6^2 * 7^3: Similar to expression 3, this expression involves multiplying two exponential expressions with different bases. Therefore, the Product Rule of Exponents is not applicable here.
In conclusion, the expression that correctly uses the Product Rule of Exponents is: 10^8 * 10^8.