Simplifying Radicals Problem
(-8)-4/3 We know that -8 may be presented as 2-3.
(-23)-4/3 Therefore, we rewrite our expression and present -8 as a prime to a power.
-23*-4/3 There is no need for the brackets, and we can use the Power Rule to find the product of inner and outer exponents.
3 * (-4/3) = -4 The outcome of the multiplication is the negative exponent -4.
-2-4 Thus, we have.
1/-24 Since the negative exponent means the reciprocal of a base number with the positive exponent, we gain the following expression. As 1 may be presented as 20, we can check our result using the Quotient Rule. Really: - 20/-24 => 0 - 4 = -4.
(-2)4 = 16. Finally, we obtain 1/16.
Problem 2 (#48)
We can rewrite our expression using rational exponents. Every n-th root may be converted into an 1/n exponent.
21/3((12x)1/3 - (2x)1/3) After substitution radicals by exponents
21/3121/3x1/3 - 21/321/3x1/3 The next step is to open the brackets.
241/3x1/3 - 41/3x1/3 Then, we apply the Product Rule.
x1/3(241/3 - 41/3) As 24 and 4 are real numbers, we can find their principal roots
241/3 ≈ 2.884, 41/3 ≈ 1.587
x1/3(2.884 - 1.587) = 1.297x1/3 The final result looks like …
