Evaluate the left hand side to find the value of aa in the equation in simplest form.

Question

x, start superscript, one third, end superscript, x, start superscript, one half, end superscript, equals, x, to the power a
x
3
1
​

x
2
1
​

=
x
a

Answer 1

To solve for a, we need to find a common base for the exponents on the left side of the equation. We can rewrite the equation as:

x^(1/3 * 2) = x^a

Simplify the left hand side:

x^(2/3) = x^a

Since the bases are the same, we set the exponents equal to each other:

2/3 = a

Therefore, the value of a is 2/3.