Which of the following correctly used the Product Rule of Exponents to simplify the expression 100*8 X 100*7 pls explain
To simplify the expression 100^8 * 100^7 using the Product Rule of Exponents, we add the exponents together.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 100.
So, 100^8 * 100^7 can be simplified as 100^(8+7).
Adding the exponents, we get 100^15.
Therefore, the expression is simplified as 100^15.
Question
Find the numerical equivalent of 10*2 ⋅10*3
To find the numerical equivalent of 10^2 * 10^3, we can apply the Product Rule of Exponents.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 10.
So, 10^2 * 10^3 can be simplified as 10^(2+3).
Adding the exponents, we get 10^5.
Therefore, the numerical equivalent of 10^2 * 10^3 is 100,000.
Find the numerical equivalent of 4*9⋅4*−7
To find the numerical equivalent of 4^9 * 4^(-7), we can again apply the Product Rule of Exponents.
The Product Rule of Exponents states that when multiplying two numbers with the same base, you add the exponents.
In this case, the base is 4.
So, 4^9 * 4^(-7) can be simplified as 4^(9+(-7)).
Adding the exponents, we get 4^2.
Therefore, the numerical equivalent of 4^9 * 4^(-7) is 16.
Which expression is correctly developed to use the Product Rule of Exponents?
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.
This expression is correct because both terms have the same base (10), and according to the Product Rule of Exponents, when multiplying two numbers with the same base, we add the exponents. In this case, the exponents are both 8, so we can simplify the expression by adding the exponents: 10^(8+8) = 10^16.
Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32
.
The Quotient Rule of Exponents states that when dividing two numbers with the same base, you subtract the exponents.
In this case, the base is 23.
So, to simplify 23^65 ÷ 23^32, we subtract the exponents: 65 - 32.
This equals 23^33.
Therefore, the simplified expression is 23^33.
Question
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?