Question
What is the quotient rule of integer exponents?
A. π^a/π^b = π^ab
B. π^a/π^b = π^b–a
C. π^a/π^b = π^a+b
D. π^a/π^b = π^a–b
A. π^a/π^b = π^ab
B. π^a/π^b = π^b–a
C. π^a/π^b = π^a+b
D. π^a/π^b = π^a–b
Answers
GPT 3.5
The quotient rule of integer exponents is: π^a/π^b = π^a-b.
Therefore, the correct answer is D.
Therefore, the correct answer is D.
Lapis
Simplify π^675/π^453
GPT 3.5
To simplify π^675/π^453, we can use the quotient rule of integer exponents, which states that π^a/π^b = π^(a-b).
Therefore, π^675/π^453 can be simplified to π^(675-453) = π^222.
Therefore, π^675/π^453 can be simplified to π^(675-453) = π^222.
Lapis
What is the missing exponent in the following equation? e^?/e^65 = e^38
GPT 3.5
Given that e^?/e^65 = e^38, we can apply the quotient rule of exponents which states that e^a/e^b = e^(a-b).
In this case, we have e^?/e^65 = e^38.
Therefore, the missing exponent is 65-38, which is equal to 27.
Therefore, e^? is e^27.
In this case, we have e^?/e^65 = e^38.
Therefore, the missing exponent is 65-38, which is equal to 27.
Therefore, e^? is e^27.
Lapis
Simplify 13^12 divided by 13^-10
GPT 3.5
To simplify 13^12 divided by 13^-10, we use the quotient rule of exponents:
13^12 / 13^-10 = 13^(12- (-10)) [subtracting exponents]
13^(12 + 10) = 13^22
Therefore, 13^12 divided by 13^-10 simplifies to 13^22.
13^12 / 13^-10 = 13^(12- (-10)) [subtracting exponents]
13^(12 + 10) = 13^22
Therefore, 13^12 divided by 13^-10 simplifies to 13^22.
Lapis
Simplify 4^13 divided by 3^-5
GPT 3.5
To simplify 4^13 divided by 3^-5, we can rewrite it as (4^13)/(1/3^5).
Recall that when dividing with the same base, we subtract the exponents:
4^13 / (1 / 3^5) = 4^13 * 3^5
To further simplify, let's calculate each exponent:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864
3^5 = 3 * 3 * 3 * 3 * 3 = 243
Now, we can substitute these values back into the equation:
4^13 * 3^5 = 67,108,864 * 243 = 16,281,282,432.
Therefore, 4^13 divided by 3^-5 simplifies to 16,281,282,432.
Recall that when dividing with the same base, we subtract the exponents:
4^13 / (1 / 3^5) = 4^13 * 3^5
To further simplify, let's calculate each exponent:
4^13 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 67,108,864
3^5 = 3 * 3 * 3 * 3 * 3 = 243
Now, we can substitute these values back into the equation:
4^13 * 3^5 = 67,108,864 * 243 = 16,281,282,432.
Therefore, 4^13 divided by 3^-5 simplifies to 16,281,282,432.
Lapis
Simplify this expression using the quotient rule of integer exponents: t^400/t^100
GPT 3.5
Using the quotient rule of integer exponents, we subtract the exponents:
t^400 / t^100 = t^(400-100) = t^300.
Therefore, the simplified expression is t^300.
t^400 / t^100 = t^(400-100) = t^300.
Therefore, the simplified expression is t^300.
Lapis
Simplify a^67/b^34
GPT 3.5
To simplify a^67/b^34, we can use the quotient rule of integer exponents:
a^67 / b^34 = a^(67-34) / b^34 = a^33 / b^34.
Therefore, the simplified expression is a^33 / b^34.
a^67 / b^34 = a^(67-34) / b^34 = a^33 / b^34.
Therefore, the simplified expression is a^33 / b^34.
Lapis
Apply the quotient rule of integer exponents to simplify 23^65 divided by 23^32
GPT 3.5
Applying the quotient rule of integer exponents, we subtract the exponents:
23^65 / 23^32 = 23^(65-32) = 23^33.
Therefore, the simplified expression is 23^33.
23^65 / 23^32 = 23^(65-32) = 23^33.
Therefore, the simplified expression is 23^33.
Lapis
Simplify this expression using the quotient rule of integer exponents: 12^53 divided by 7^53
GPT 3.5
To simplify 12^53 divided by 7^53 using the quotient rule of integer exponents, we subtract the exponents:
12^53 / 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
12^53 / 7^53 = (12/7)^53.
Therefore, the simplified expression is (12/7)^53.
Lapis
Which are the correct steps to follow to simplify an exponential expression using the quotient rule of integer exponents?
A. 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.
B. Check if the bases are different, if they are subtract, exponents of the numerator and denominator, and write the resulting expression in the exponential form.
C. Subtract exponents of the numerator and denominator and write the resulting expression in exponential form.
D. Check if the bases are the same as they are at the exponent of the numerator and denominator, leave as is otherwise, and write the resulting expression in exponential form.
A. 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.
B. Check if the bases are different, if they are subtract, exponents of the numerator and denominator, and write the resulting expression in the exponential form.
C. Subtract exponents of the numerator and denominator and write the resulting expression in exponential form.
D. Check if the bases are the same as they are at the exponent of the numerator and denominator, leave as is otherwise, and write the resulting expression in exponential form.
GPT 3.5
The correct steps to follow to simplify an exponential expression using the quotient rule of integer exponents are:
C. Subtract exponents of the numerator and denominator and write the resulting expression in exponential form.
Therefore, the correct answer is C.
C. Subtract exponents of the numerator and denominator and write the resulting expression in exponential form.
Therefore, the correct answer is C.