Use the properties of exponents to determine the value of a for the equation:

Question

(x⁵)^(1/4)3√x = x^a

The 3 goes on the index of the square root.

Answer 1

Your 3√x is the cubic root of x. It can also be represented by x^1/3. If we perform this substitution, the equation becomes:

(x⁵)^(1/4)x^1/3 = x^a

Since (x^a)^b = x^ab, we can combine the two first exponents into:

x^5/4x^1/3 = x^a

Since x^ax^b = x^a+b, we can combine the two terms:

x^5/4+1/3 = x^a

Since our bases are both x, it follows that the exponents must be equal:

5/4 + 1/3 = a

15/12 + 4/12 = a

19/12 = a