Q.Simplify: $2^3 \times 2^4$.

Multiplying two powers of the same base means adding the indices.

By the product law, $2^3\times2^4=2^{3+4}=2^7=128$.

By the product law of indices (same base $2$), add the exponents:

Evaluating: $2^7 = 2\times2\times2\times2\times2\times2\times2 = 128$.

Check (independent recomputation): compute each factor separately first — $2^3=8$ and $2^4=16$; then $8\times16=128$, exactly matching $2^7$.

Multiplying the exponents instead of adding them (wrongly computing $2^{3\times4}=2^{12}$), a confusion with the power-of-a-power law rather than the product law.