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What is a rational exponent?
A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root. For example, ( a^{\frac{m}{n}} ) means the ( n )-th root of ( a ) raised to the power of ( m ), or ( \sqrt[n]{a^m} ). Rational exponents allow for a more concise representation of roots and powers in mathematical expressions.
Do all rational functions have holes?
Not all rational functions have holes. A rational function is a ratio of two polynomials, and holes occur at points where both the numerator and denominator equal zero, indicating a common factor. If a rational function has no common factors between the numerator and denominator, it will not have any holes, although it may have vertical asymptotes or other features.
Which statement is true Converting an integer to a fraction shows whether it is rational A negative fraction is never rational An integer numerator over a zero denominator is never rational?
Statement 1 is true but totally unnecessary. As integer is always a rational and you do not need to convert it to a fraction to determine whether or not it is rational. A negative fraction is can be rational or irrational. The fact that it is negative is irrelevant to its rationality. An integer number over a zero denominator is not defined and so cannot be rational or irrational or anything. It just isn't.
Is a negative integer a rational number?
Absolutely. As long as it can be expressed as a fraction with the denominator not being zero, and both numerator and denominator being integers.
What is a rational exponent in math?
If the exponent or raised power of a number is in the form of p/q the exponent is said to be rational exponent. For example= 11/2 22/3
How can a rational number be positive?
A rational number is simply a number that can be expressed as a fraction, with integer numerator and denominator. Such a number can be positive, negative, or zero.A rational number is simply a number that can be expressed as a fraction, with integer numerator and denominator. Such a number can be positive, negative, or zero.A rational number is simply a number that can be expressed as a fraction, with integer numerator and denominator. Such a number can be positive, negative, or zero.A rational number is simply a number that can be expressed as a fraction, with integer numerator and denominator. Such a number can be positive, negative, or zero.
Is -15 rational or irrational?
Any integer, whether positive or negative, is a rational number. It can be expressed as a fraction with a negative numerator and a denominator of 1.
Why is -6 rational?
All integers, including negative integers, are rational. They can all be expressed as a fraction with the denominator 1.
How do you simplify numbers when they have a negative rational exponent?
A negative exponent is simply the reciprocal.A rational exponent of the form p/q is the qth root of the pth power.So for example,x^(-2/3) = 1/x^(2/3) = 1/cuberoot(x^2) or, equivalently, 1/[cuberoot(x)]^2
Negative fractions are Rational number?
They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.
When subtracting rational expressions with a common denominator always remember to the negative sign?
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Which statement is true Converting an integer to a fraction shows whether it is rational A negative fraction is never rational An integer numerator over a zero denominator is never rational?
Statement 1 is true but totally unnecessary. As integer is always a rational and you do not need to convert it to a fraction to determine whether or not it is rational. A negative fraction is can be rational or irrational. The fact that it is negative is irrelevant to its rationality. An integer number over a zero denominator is not defined and so cannot be rational or irrational or anything. It just isn't.
Is a negative integer a rational number?
Absolutely. As long as it can be expressed as a fraction with the denominator not being zero, and both numerator and denominator being integers.
What is a rational exponent in math?
If the exponent or raised power of a number is in the form of p/q the exponent is said to be rational exponent. For example= 11/2 22/3
Distinguish between a pole and an essential singularity?
If the Laurent series has only finitely many terms with negative powers of z - c, then the singularity is a pole. The biggest negative exponent is the order of the pole. Example: Singularities of rational functions with no common factors in its numerator and denominator. (These come from setting the denominator equal to 0.) If the Laurent series has infinitely many terms with negative powers of z - c, then the singularity is essential. Example: e^(1/z) = 1 + (1/z) + (1/2!) 1/z^2 + ... has an essential singularity at z = 0.
Can a rational number be negative in the denominator?
Yes. It can also be negative in the numerator. Both positive and negative numbers (as well as zero) can be rational numbers. Both positive and negative numbers can be irrational numbers. Both positive and negative numbers (as well as zero) can be integers.
In rational functions what happens when w gets close to zero?
The answer depends on what w represents. If w is the denominator of the rational function then as w gets close to zero, the rational function tends toward plus or minus infinity - depending on the signs of the dominant terms in the numerator and denominator.
