Question

15. Use your knowledge of fractional exponents to show that the following

statement is true: The square root of the cube root of a number equals
the sixth root of that number.

Answer 1

Step-by-step explanation:

((X)^1/2 )^1/3 = x^(1/2 ×1/3)= x^1/6

that what you need to prove

Answer 2

The square root of the cube root of a number equals the sixth root because when you raise a power to another power (in this case, (x^(1/3))^(1/2)), you multiply the exponents, resulting in x^(1/6), which represents the sixth root of a number.

Step-by-step explanation:

Understanding Fractional Exponents in Mathematics

To show that the square root of the cube root of a number equals the sixth root of that number, let us use fractional exponents. Considering a number x, the cube root of x is represented as x1/3.

The square root of the cube root of x would then be (x1/3)1/2. According to the properties of exponents, when raising a power to another power, you multiply the exponents. Thus,

(x1/3)1/2 = x1/3 × 1/2 = x1/6,

which is precisely the sixth root of x. This demonstration uses the general exponential rule that (am)n = am × n, as illustrated in previous examples with different bases and exponents.