Explain why rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is negative.
Answers
Answer:
Step-by-step explanation:
A rational exponent is an exponent that is a fraction. If the fraction has an even denominator, the root will be of an even number (like the square root, the 4th root, etc.). ... So, you can't take the square root of a negative number because it is impossible to get a negative number when squaring!
Answer:
What does "exponential" mean?
You should start by explaining what the exponent is called. Here is the appropriate definition.
Exponent - It is finding the value of the power of a number.
Thus, finding the power of a number a with the exponent r and raising the number a to the degree r are the same thing. For example, if the problem is "Calculating the value of degree (0.5) 5", it can be reformulated as: "Raise the number 0.5 to the power of 5".
Now you can go directly to the rules by which exponentiation is performed.
fractional exponent
Let's begin the investigation of this issue with a specific example. 43/2. What do 3/2 degrees mean? 3 - numerator, means to increase a number (in this case 4) to a cube. The number 2 is the denominator, it is the extraction of the second root of the number (4 in this case).
Then we get the square root of 43 = 2^3 = 8. Answer: 8.
So, the denominator of a fractional degree can be either 3 or 4 and any number up to infinity, and this number determines the degree of the square root derived from a given number. Of course, the denominator cannot be zero.
A rational exponent is an exponent that is a fraction. If the fraction has an even denominator, the root will be of an even number (like the square root, the 4th root, etc.). ... So, you can't take the square root of a negative number because it is impossible to get a negative number when squaring!