Quotient Rule of Exponents Quick Check
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Simplify this expression using the Quotient Rule of Integer Exponents: t^400 t^100.(1 point)
Responses
t^500
t^300
t^4
300
Simplify a^67/b^34.(1 point)
ab^33
23
a^33
a^67 / b^34
Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32.(1 point)
Responses
23^33
97
23^97
1^33
Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53.(1 point)
Responses
5^106
12^106
12^53÷7^53
5^53
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
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, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
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.
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.
what is the correct answer to all 5 questions
1. Simplify this expression using the Quotient Rule of Integer Exponents: t^400 t^100.
- The correct answer is t^500.
2. Simplify a^67/b^34.
- The correct answer is a^33.
3. Apply the Quotient Rule of Integer Exponents to simplify 23^65÷23^32.
- The correct answer is 23^33.
4. Simplify this expression using the Quotient Rule of Integer Exponents: 12^53÷7^53.
- The correct answer is 12^53÷7^53.
5. Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
- The correct steps are to check if the bases are the same; if they are, subtract the exponents of the numerator and denominator and write the resulting expression in exponential form.
All of that was correct except question 1. The correct answer to question 1 is T^300, NOT T^500.
The correct answers to the given questions are as follows:
1. Simplify this expression using the Quotient Rule of Integer Exponents: t^400 t^100.
Answer: t^500
To simplify this expression using the Quotient Rule of Integer Exponents, you need to add the exponents when dividing two variables with the same base. In this case, both terms have the base 't'. So, you add the exponents of 't' which gives you t^(400+100) = t^500.
2. Simplify a^67/b^34.
Answer: a^33 / b^34
To simplify this expression using the Quotient Rule of Integer Exponents, you subtract the exponent of the denominator from the exponent of the numerator. So, a^67 / b^34 simplifies to a^(67-34) / b^34, which is equal to a^33 / b^34.
3. Apply the Quotient Rule of Integer Exponents to simplify 23^65 ÷ 23^32.
Answer: 23^33
To simplify this expression using the Quotient Rule of Integer Exponents, you subtract the exponent of the denominator from the exponent of the numerator. So, 23^65 ÷ 23^32 simplifies to 23^(65-32) = 23^33.
4. Simplify this expression using the Quotient Rule of Integer Exponents: 12^53 ÷ 7^53.
Answer: 12^53 ÷ 7^53
This expression cannot be simplified further using the Quotient Rule of Integer Exponents because the bases (12 and 7) are different. Therefore, the expression remains as 12^53 ÷ 7^53.
5. Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?
Answer: 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.
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are to first check if the bases are different. If they are indeed different, then you subtract the exponents of the numerator and denominator and write the resulting expression in exponential form.
1. t^500
2. a^67 / b^34
3. 23^33
4. 12^53 / 7^53
5. Subtract the exponents of the numerator and denominator (leave as-is if the bases are different); and write the resulting expression in exponential form.