If 2a = (32)1/3, then a is equal to:

When two powers with the same base are equal, their exponents must be equal — so to solve for an unknown exponent, first rewrite both sides as powers of one common base.

1. Express 32 as a power of 2: 32 = 25.

2. Substitute into the equation: 2a = (25)1/3.

3. Apply the power-of-a-power rule (multiply the exponents): (25)1/3 = 25/3.

4. Both sides now share the base 2: 2a = 25/3.

5. Since the bases match, equate the exponents directly: a = 5/3.

Check: cubing 25/3 gives 25 = 32, which matches (32)1/3 cubed back to 32 — confirming the value is consistent.

So a = 5/3.