llaffer
Favorite Answer
I think that is:
∛(x⁵) / (x²)^(2/3) = xᵃ
The first thing I'll do is turn the cube root into a fraction exponent. Since it's a cube root the denominator is 3:
x^(5/3) / (x²)^(2/3) = xᵃ
Next, I'll look at the denominator. The exponent of an exponent is the same as the product of exponents. This gives us:
x^(5/3) / x^(2 * 2/3) = xᵃ
x^(5/3) / x^(4/3) = xᵃ
Now we have the quotient of two numbers with the same base. This can be simplified by getting the difference of the two exponents:
x^(5/3 - 4/3) = xᵃ
x^(1/3) = xᵃ
Finally, we have two values that are the same with the same bases so the exponents must be equal:
a = 1/3