Find the numerical equivalent of 7^2⋅7^3(1 point)
To find the numerical equivalent of 7^2⋅7^3, we can simplify the expression by adding the exponents together. So, 7^2⋅7^3 is equivalent to 7^(2+3), which is equal to 7^5.
To calculate 7^5, we multiply 7 by itself 5 times:
7^5 = 7 × 7 × 7 × 7 × 7 = 16807.
Therefore, the numerical equivalent of 7^2⋅7^3 is 16807.
Find the numerical equivalent of 3^9⋅3^−5(1 point)
To find the numerical equivalent of 3^9⋅3^−5, we can simplify the expression by subtracting the exponents.
3^9⋅3^(-5) is equivalent to 3^(9-5), which is equal to 3^4.
To calculate 3^4, we multiply 3 by itself 4 times:
3^4 = 3 × 3 × 3 × 3 = 81.
Therefore, the numerical equivalent of 3^9⋅3^(-5) is 81.
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
10^8⋅10^8
32^7
(5^2)^9
6^2⋅7^3
The expression that is correctly developed to use the Product Rule of Exponents is 6^2⋅7^3.
Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7?(1 point)
Responses
100^15
10,000^15
100^56
200^15
The correct answer is 100^15. When using the Product Rule of Exponents, you add the exponents when you have the same base. In this case, both exponents are 8 and 7. Adding these two exponents together gives us 15. Therefore, 100^8⋅100^7 simplifies to 100^15.
Find the numerical equivalent of 10^2 ⋅10^3(1 point)
Responses
10^5
100,000
100,000
1,100
1,100
10
To find the numerical equivalent of 10^2⋅10^3, we can simplify the expression by adding the exponents together.
10^2⋅10^3 is equivalent to 10^(2+3), which is equal to 10^5.
Therefore, the numerical equivalent of 10^2⋅10^3 is 100,000.
Find the numerical equivalent of 2^5 • 2^-2
To find the numerical equivalent of 2^5 • 2^-2, we can apply the Product Rule of Exponents, which states that when multiplying two numbers with the same base, we add the exponents.
For 2^5 • 2^-2, we have the base 2 and two exponents, 5 and -2.
Adding the exponents, 5 + (-2) = 3.
Therefore, 2^5 • 2^-2 is equivalent to 2^3.
To calculate 2^3, we multiply 2 by itself 3 times:
2^3 = 2 • 2 • 2 = 8.
Therefore, the numerical equivalent of 2^5 • 2^-2 is 8.
Find the numerical equivalent of 4^9 • 4^-7?
To find the numerical equivalent of 4^9 • 4^-7, we can apply the Product Rule of Exponents, which states that when multiplying two numbers with the same base, we add the exponents.
For 4^9 • 4^-7, we have the base 4 and two exponents, 9 and -7.
Adding the exponents, 9 + (-7) = 2.
Therefore, 4^9 • 4^-7 is equivalent to 4^2.
To calculate 4^2, we multiply 4 by itself 2 times:
4^2 = 4 • 4 = 16.
Therefore, the numerical equivalent of 4^9 • 4^-7 is 16.
Simplify this expression using the Quotient Rule of Integer Exponents : t^400/ t^100?
To simplify the expression t^400/ t^100 using the Quotient Rule of Exponents, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, the numerator has an exponent of 400 and the denominator has an exponent of 100.
Subtracting the exponent of the denominator from the exponent of the numerator, we have 400 - 100 = 300.
Therefore, t^400/ t^100 simplifies to t^300.
Apply the Quotient Rule of integer Exponents to simplify 23^65 divided by 23^32?
To simplify 23^65 divided by 23^32 using the Quotient Rule of Integer Exponents, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, both numbers have the base 23. So, we subtract the exponent of the denominator, 32, from the exponent of the numerator, 65.
65 - 32 = 33.
Therefore, 23^65 divided by 23^32 simplifies to 23^33.
Simplify this expression using the Quotient Rule of Integer Exponents :12^53 divided 7^53?
To simplify 12^53 divided by 7^53 using the Quotient Rule of Integer Exponents, you subtract the exponent of the denominator from the exponent of the numerator.
In this case, we have 12^53 divided by 7^53.
Subtracting the exponent of the denominator from the exponent of the numerator, we have 53 - 53 = 0.
Therefore, 12^53 divided by 7^53 simplifies to 1.
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
To simplify an exponential expression using the Quotient Rule of Integer Exponents, you can follow these steps:
1. Identify the base of the exponential expression. This is the number that is raised to a certain exponent.
2. Determine the exponent of the numerator and the exponent of the denominator.
3. Apply the Quotient Rule of Integer Exponents, which states that when dividing two exponential expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
4. Subtract the exponent of the denominator from the exponent of the numerator.
5. Simplify the expression by writing the new exponent in the numerator and keeping the base the same.
6. Verify if there are any further simplification steps possible, such as reducing fractions or factoring out common terms.
By following these steps, you can simplify exponential expressions using the Quotient Rule of Integer Exponents.