1. The denominator of a fractional exponent represents the __.
2. Taking a cube root of an expression is the same as raising it to the __ power.
Assuming
You have
9^(3/2)=(√9)³
the numerator expresses the power of the index...the denominator expresses the root of the index
Q.2
∛(a)=(a)^⅓
1. The denominator of a fractional exponent represents the root that is being taken. For example, in the expression x^(1/2), the denominator 2 represents the square root of x.
2. Taking a cube root of an expression is the same as raising it to the 1/3 power. So, if we have an expression x, taking the cube root of x can be written as x^(1/3).
1. The denominator of a fractional exponent represents the root of the base. Specifically, if we have an exponent in the form of 1/n, where n is a positive integer, it means taking the nth root of the base.
To understand this concept better, let's consider an example. Suppose we have the expression 4^(1/2). Here, the numerator of the fractional exponent is 1, and the denominator is 2. In this case, the denominator tells us to take the square root of the base, which is 4. Therefore, 4^(1/2) is equal to the square root of 4, which is 2.
2. Taking a cube root of an expression is the same as raising it to the 1/3 power.
To understand why this is the case, let's consider an example. Suppose we have the expression 8^(1/3). Here, the numerator of the fractional exponent is 1, and the denominator is 3. In this case, the denominator tells us to take the cube root of the base, which is 8. Therefore, 8^(1/3) is equal to the cube root of 8, which is 2.