Using the Quotient Rule of Exponents, what is the exponent of 39÷37 when it is in exponential simplest form
To use the quotient rule of exponents, we subtract the exponents of the numerator and denominator.
The exponent of 39 is 1, and the exponent of 37 is also 1. Therefore, we have:
39 ÷ 37 = (3^1)(7^1) ÷ (3^1)(7^1)
According to the quotient rule, we subtract the exponents:
1 - 1 = 0
Therefore, the exponent of 39 ÷ 37 when it is in exponential simplest form is 0.
To find the exponent of 39÷37 in exponential simplest form using the Quotient Rule of Exponents, we can express the division as a fraction.
The Quotient Rule of Exponents states that when dividing two numbers with the same base, you subtract the exponents.
So, we can rewrite 39÷37 as (39/37)^1, where the base is 39/37 and the exponent is 1.
In exponential simplest form, the exponent is 1. Therefore, the exponent of 39÷37 when it is in exponential simplest form is 1.
To find the exponent when the quotient 39 ÷ 37 is expressed in exponential simplest form, we can use the Quotient Rule of Exponents.
The Quotient Rule of Exponents states that when dividing two numbers with the same base, we subtract the exponents.
In this case, we have 39 ÷ 37. Since both 39 and 37 have the same base, which is implied to be 10, we can subtract their exponents.
Now, we need to express 39 and 37 in exponential form. To express a number in exponential form, we need to find the power or exponent that would result in that number when applied to the base.
For 39, we can write it as 10^x = 39. We need to find what value of x satisfies this equation. To do this, we can take the logarithm of both sides using the base 10 logarithm.
log10(39) = x
Using a calculator, we find that log10(39) ≈ 1.5911. So, we can approximate the exponent of 39 as 1.5911.
For 37, we can follow the same steps:
10^y = 37
log10(37) = y
Using a calculator again, we find that log10(37) ≈ 1.5682. So, the exponent of 37 is approximately 1.5682.
Now, we can apply the Quotient Rule of Exponents and subtract the exponents:
exponent of 39 ÷ 37 = (exponent of 39) - (exponent of 37)
≈ 1.5911 - 1.5682
Calculating this, we find that the exponent of 39 ÷ 37, when simplified, is approximately 0.0229.