Simplify x^675/^453
To simplify the expression, we can use the fact that x^a / x^b = x^(a-b).
Therefore, x^675 / x^453 can be written as x^(675-453) = x^222.
So, x^675 / x^453 simplifies to x^222.
What is the missing exponent in the following equation?
e^?/e^65 = e^38
To find the missing exponent, we can use the fact that e^a / e^b = e^(a-b).
Therefore, e^? / e^65 = e^38 can be rewritten as e^(?-65) = e^38.
If two exponential expressions with the same base are equal, then their exponents must also be equal.
Therefore, we have ? - 65 = 38.
Solving for ?, we add 65 to both sides: ? = 38 + 65 = 103.
So, the missing exponent in the equation is 103.
In summary, e^? / e^65 = e^38 is equivalent to e^103 / e^65 = e^38.
13^12 ÷ 13^-10
When dividing two numbers with the same base, subtract the exponents.
Therefore, we have:
13^12 ÷ 13^(-10) = 13^(12 - (-10)) = 13^(12 + 10) = 13^22.
So, 13^12 ÷ 13^(-10) simplifies to 13^22.
4^13 ÷ 3^-5
When dividing two numbers with the same base, subtract the exponents.
Therefore, we have:
4^13 ÷ 3^(-5) = 4^13 ÷ 1 / 3^5 = 4^13 × 3^5.
To multiply two numbers with the same base, add the exponents.
Therefore, we have:
4^13 × 3^5 = 4^13 × 3^5 = 4^(13+5) × 3^5 = 4^18 × 3^5.
So, 4^13 ÷ 3^(-5) simplifies to 4^18 × 3^5.
Simplify this expression using the Quotient Rule of Integer Exponents: t400/t100 .(1 point)
Responses
30
t^300
t^4
t^500
According to the Quotient Rule of Integer Exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, t^400 / t^100 can be simplified as t^(400-100) = t^300.
So, the simplification of t^400 / t^100 using the Quotient Rule of Integer Exponents is t^300.
Simplify a^67/b^34 .(1 point)
Responses
ab^33
23
a^67/b^34
a^33
To simplify a^67/b^34, we can use the Quotient Rule of Exponents. According to this rule, when dividing two powers with the same base, we subtract the exponents.
Therefore, a^67/b^34 simplifies to a^(67-34)/b^(34-34) = a^33/b^0.
Any non-zero number raised to the exponent of 0 is equal to 1. Thus, b^0 = 1.
Therefore, a^33/b^0 simplifies to a^33/1 = a^33.
So, the simplified form of a^67/b^34 is a^33.
Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32 .(1 point)
Responses
97
23^33
1^33
23^97
According to the Quotient Rule of Integer Exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, 23^65 ÷ 23^32 can be simplified as 23^(65-32) = 23^33.
So, the simplification of 23^65 ÷ 23^32 using the Quotient Rule of Integer Exponents is 23^33.
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53 .(1 point)
Responses
5^53
12^53÷7^53
5^106
12^106
According to the Quotient Rule of Integer Exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, 12^53 ÷ 7^53 can be simplified as 12^(53-53) ÷ 7^(53-53) = 12^0 ÷ 7^0.
Any non-zero number raised to the exponent of 0 is equal to 1. Thus, 12^0 and 7^0 are both equal to 1.
Therefore, 12^53 ÷ 7^53 simplifies to 1 ÷ 1 = 1.
So, the simplified form of 12^53 ÷ 7^53 using the Quotient Rule of Integer Exponents is 1.
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53
According to the Quotient Rule of Integer Exponents, when dividing two powers with the same base, you subtract the exponents.
Therefore, 12^53 ÷ 7^53 can be simplified as (12/7)^53.
So, the simplified form of 12^53 ÷ 7^53 using the Quotient Rule of Integer Exponents is (12/7)^53.
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 should follow these steps:
1. Identify the base of the exponential expressions. The base refers to the common factor in both the numerator and denominator.
2. Apply the Quotient Rule, which states that when dividing two powers with the same base, you can subtract the exponents.
3. Subtract the exponent of the denominator from the exponent of the numerator. This will give you the exponent of the simplified expression.
4. Keep the base the same and use the exponent you found in the previous step. This will give you the simplified exponential expression.
By following these steps, you can simplify the given exponential expression using the Quotient Rule of Integer Exponents.
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.