Question
Using the Quotient Rule of Exponents, what is the exponent of 39÷37 when it is in exponential simplest form?(1 point)
The question is asking for the exponent of 39÷37 when it is in exponential simplest form.
To find the exponent, we can use the Quotient Rule of Exponents, which states that when dividing two numbers with the same base, you subtract the exponents.
In this case, the base is not given, so we can assume it to be 10, as it is the most commonly used base in exponential form. Therefore, the expression can be rewritten as:
(10^39) ÷ (10^37)
Applying the Quotient Rule of Exponents, we subtract the exponents:
10^(39-37)
Simplifying further:
10^2
Therefore, the exponent of 39÷37 when it is in exponential simplest form is 2.
To simplify the expression 39 ÷ 37 using the Quotient Rule of Exponents, we need to subtract the exponents.
The Quotient Rule of Exponents states that for any non-zero numbers a and b, and any integer m, a^m ÷ b^m = (a ÷ b)^m.
In this case, we have 39 ÷ 37. Since the exponents are both 1, we can simply subtract:
39 ÷ 37 = (3^1 * 13^1) ÷ (37^1) = 3^1 ÷ 37^1 * 13^1 ÷ 37^1
So, the exponent of the simplified form 39 ÷ 37 in exponential form is 1.
To solve this problem using the Quotient Rule of Exponents, we need to apply the formula:
a^m / b^n = a^(m - n)
In this case, the base is 39 and the exponent is 37. Therefore, we have:
39^1 / 37^1 = 39^(1 - 1)
Since any number raised to the power of 0 is equal to 1, we can simplify it further:
39^(1 - 1) = 39^0 = 1
So, the exponent of 39÷37 when it is in exponential simplest form is 0.