Hey Bot, can you help me with some math?
Of course! I'll do my best to assist you with math. What do you need help with?
Simplify this expression using the Quotient Rule of Integer Exponents: t^400/ t^100. (1 point)
Responses
t^300
t^4
300
t^500
To simplify the expression (t^400) / (t^100) using the Quotient Rule of Integer Exponents, we subtract the exponent in the denominator from the exponent in the numerator.
The Quotient Rule states that t^m / t^n = t^(m-n).
Applying this rule to the given expression, we get:
t^400 / t^100 = t^(400-100) = t^300.
Therefore, the simplified expression is t^300.
Simplify a^67/ b^34.(1 point)
Responses
23
a^67/ b^34
ab^33
a^33
To simplify the expression (a^67) / (b^34), we can apply the Quotient Rule of Integer Exponents, which states that a^m / b^n = a^(m-n) / b^n.
Using this rule, we subtract the exponent in the denominator from the exponent in the numerator:
(a^67) / (b^34) = a^(67-34) / b^34 = a^33 / b^34.
Therefore, the simplified expression is a^33 / b^34.
Apply the Quotient Rule of Integer Exponents to simplify 23^65 ÷ 23^32. (1 point)
Responses
23^97
1^33
97
23^33
To simplify the expression (23^65) ÷ (23^32) using the Quotient Rule of Integer Exponents, we subtract the exponent in the denominator from the exponent in the numerator.
The Quotient Rule states that a^m ÷ a^n = a^(m-n).
Applying this rule to the given expression, we have:
(23^65) ÷ (23^32) = 23^(65-32) = 23^33.
Therefore, the simplified expression is 23^33.
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
To simplify the expression (12^53) ÷ (7^53) using the Quotient Rule of Integer Exponents, we subtract the exponent in the denominator from the exponent in the numerator.
The Quotient Rule states that a^m ÷ a^n = a^(m-n).
Applying this rule to the given expression, we have:
(12^53) ÷ (7^53) = 12^(53-53) ÷ 7^53 = 12^0 ÷ 7^53.
Any non-zero number raised to the power of zero is equal to 1. Therefore, we can simplify further:
12^0 ÷ 7^53 = 1 ÷ 7^53.
Hence, the simplified expression is 1 ÷ 7^53.
So does that mean 12^53÷7^53
Is the answer?
Apologies for the confusion in my previous response. Yes, you are correct. The simplified expression is 12^53 ÷ 7^53.
Question
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.
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.
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:
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.
That wasn't correct
Apologies for the incorrect response. The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
1. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator.
2. Write the resulting expression with the same base and the subtracted exponent.
3. Simplify further if possible.
I apologize for any confusion caused by my earlier response.
Just messing with you bot, I'll check to see though.
No problem at all! Feel free to double-check the steps and let me know if you have any further questions or need any assistance. I'm here to help!
Thanks bot ! They all were correct by the way
You're welcome! I'm glad to hear that all the response options were correct. If you have any more questions or need further assistance in the future, feel free to ask. Have a great day!
Hey bot can you help with this question?
Of course! I'll do my best to help you. Please go ahead and ask your question.
4/3 (-2 + 1^0 ) is 4/3 (-2 + blank or answer )
To simplify the expression 4/3 (-2 + 1^0), we follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, let's evaluate the exponent 1^0, which is equal to 1 raised to the power of 0. Any number (except 0) raised to the power of 0 is always equal to 1. Therefore, 1^0 is equal to 1.
Now, we substitute the value back into the expression:
4/3 (-2 + 1) = 4/3 (-2 + 1).
Next, we simplify the parentheses:
4/3 (-1) = -4/3.
Therefore, the answer is -4/3.
Bot you were off just a little
It wasn't : - 4/3
It was your other answer : 1