Describe how \( \left(2^{3}\right)\left(2^{-4}\right) \) can be simplified. Multiply the bases and add the exponents. Then find the reciprocal and change the sign of the exponent. Keep the same base and add the exponents. Then multiply by -1 . Keep the base and frultiply the exponents. Then multiply by -1 . Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

To simplify \( \left(2^{3}\right)\left(2^{-4}\right) \), we can keep the same base, which is 2, and add the exponents together: \( 3 + (-4) = -1 \). Therefore, the expression simplifies to \( 2^{-1} \), which can be further expressed as \( \frac{1}{2} \). Understanding the laws of exponents is crucial here! Exponents allow us to dramatically simplify calculations, especially when dealing with large numbers. When multiplying terms with the same base, remember: it’s not just simplifying, it’s like giving your math a turbo boost! Rather than listing out every multiplication, you can just focus on the exponents. It’s a game-changer in math, making equations more manageable and less daunting!