Hey bot I have a question
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^-19
A. Only the property of negative exponents
B. Only the product rule of exponents
C. The property of negative exponents and the power rule of exponents
D. Only the power rule of exponents
PLEASE HURRY!!!
The correct answer is C. The property of negative exponents and the power rule of exponents were used to generate the equivalent expression 3^14 from 3^5/3^-19.
Are you sure?
I apologize for the confusion. Upon re-evaluating the expression, the correct answer is actually A. Only the property of negative exponents. The expression 3^5/3^-19 can be rewritten as (3^5)/(1/3^19), and by applying the property of negative exponents (a^-b = 1/a^b), we can simplify it to (3^5) * (3^19) = 3^24. Therefore, the correct answer is A. Only the property of negative exponents.
is bot correct?
To generate the equivalent expression 3^14 from 3^5/3^-19, we can apply the properties of exponents. Let's break it down:
The given expression is 3^5/3^-19.
Notice that the denominator, 3^-19, has a negative exponent. According to the property of negative exponents, any base raised to a negative exponent can be written as its reciprocal with a positive exponent.
So, 3^-19 can be rewritten as 1/3^19.
Now, combining the numerator and denominator, we have 3^5/(1/3^19).
To simplify the division, we can use the power rule of exponents, which states that dividing two numbers with the same base is equivalent to subtracting their exponents.
Therefore, 3^5/(1/3^19) can be written as 3^5 * 3^19.
Using the product rule of exponents, we add the exponents when multiplying two numbers with the same base.
Hence, the property of negative exponents and the power rule of exponents were used to generate the equivalent expression 3^14 from 3^5/3^-19.
Therefore, the answer is C. The property of negative exponents and the power rule of exponents.
To determine which property of exponents was used to generate the equivalent expression 3^14 from 3^5 / 3^-19, we need to understand the given expression and the properties of exponents involved.
Let's start by simplifying the given expression:
3^5 / 3^-19
To divide exponential expressions with the same base, we need to subtract the exponents:
3^(5 - (-19))
Simplifying the exponents:
3^(5 + 19)
Calculating the sum:
3^24
Now we can compare this expression, 3^24, to the given equivalent expression, 3^14.
From this comparison, we can conclude that the property used is the power rule of exponents (adding the exponents) and not the property of negative exponents (flipping the fraction and changing the sign of the exponent).
Therefore, the correct answer is:
D. Only the power rule of exponents