Expand the Expression: Solving 2^(2a+a) Step by Step

The product rule states that $a^m \times a^n = a^{m+n}$. When we reverse this, $a^{m+n} = a^m \times a^n$. We're splitting one exponent into a product of two powers with the same base.

Yes! You could write $2^{2a+a} = 2^{3a}$, but the question asks to expand the expression. Expanding means showing it as a product: $2^{2a} \times 2^a$.

This would equal $2^{a+a+a} = 2^{3a}$, but our original expression is $2^{2a+a} = 2^{3a}$. While both equal $2^{3a}$, the correct expansion matches the original exponent structure: $2^{2a} \times 2^a$.

Try a specific value! If a=1, then $2^{2(1)+1} = 2^3 = 8$. Check: $2^{2(1)} \times 2^1 = 2^2 \times 2^1 = 4 \times 2 = 8$ ✓

The power rule is $(a^m)^n = a^{mn}$ and applies to powers raised to powers. Here we have addition in the exponent, so we use the product rule instead.