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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?