What is the Quotient Rule of Integer Exponents?(1 point)
Responses
xaxb=xa+b
the fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A plus b power
xaxb=xa−b
the fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A minus b power
xaxb=xb−a
the fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the b minus A power
xaxb=xab
the fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A minus b power
Simplify x675x453
.(1 point)
To simplify the expression x^675 * x^453, we can use the quotient rule of integer exponents, which states that x^a * x^b = x^(a+b).
Using this rule, we can simplify the expression as follows:
x^675 * x^453 = x^(675+453) = x^1128
Therefore, the simplified expression is x^1128.
says its wrong
I apologize for the error. Let's correct it.
To simplify the expression x^675 * x^453, we can again use the quotient rule of integer exponents, which states that x^a * x^b = x^(a+b).
Using this rule, we can simplify the expression as follows:
x^675 * x^453 = x^(675+453) = x^1128
Therefore, the simplified expression is still x^1128. If this answer is marked as incorrect, please provide the correct answer or any additional information that may help me better understand the problem.
it doesn't say anything else other than Simplify x675x453
.(1 point), so idk why its wrong
I apologize for the misunderstanding. To simplify the expression x^675 * x^453, we can add the exponents together:
x^675 * x^453 = x^(675 + 453) = x^1128
So the simplified expression is x^1128. If this is marked as incorrect, please let me know and provide any further information that may help clarify the problem.
What is the missing exponent in the following equation?
e?e65 = e38
(1 point)
The missing exponent in the equation e^? * e^65 = e^38 is -27.
To solve for the missing exponent, we can use the quotient rule of integer exponents, which states that e^a / e^b = e^(a-b).
In this case, since e^? * e^65 = e^38, we can rewrite this equation as e^? / e^65 = e^38.
Therefore, we have ? - 65 = 38.
Solving for ?, we find that ? = 38 + 65 = 103.
Therefore, the missing exponent in the equation is -27.
The Quotient Rule of Integer Exponents states that when you have a fraction with a numerator that is x raised to the power of A and a denominator that is x raised to the power of B, the result is x raised to the power of A minus B.
In other words:
x^A / x^B = x^(A - B)
To understand why this rule is true, we can break it down step by step:
1. Start with x^A / x^B. This means we have x multiplied by itself A times in the numerator, and x multiplied by itself B times in the denominator.
2. When you divide two numbers with the same base, you subtract their exponents. So, in this case, we have x^(A - B) as the simplified form.
For example:
If we have x^3 / x^2, according to the Quotient Rule, we subtract the exponents: x^(3 - 2) = x^1 = x.
So, the Quotient Rule of Integer Exponents simplifies expressions involving fractions with powers of x in the numerator and denominator by subtracting the exponents.