Compute:
$-3 \cdot 2^5$
Answer (1)
First, calculate the exponent: 2 5 = 32 .
Then, multiply the result by -3: − 3 × 32 = − 96 .
The final result is − 96 .
Explanation
Understanding the Problem We are asked to compute the value of the expression − 3 × 2 5 . This involves exponentiation and multiplication.
Calculating the Exponent First, we need to calculate 2 5 , which means 2 multiplied by itself 5 times: 2 5 = 2 × 2 × 2 × 2 × 2 = 32
Performing the Multiplication Next, we multiply the result by − 3 : − 3 × 32 = − 96
Final Answer Therefore, the final result is − 96 .
Examples
Understanding how to compute expressions like this is fundamental in many areas, such as calculating compound interest or understanding exponential decay in physics. For instance, if you invest money that grows at a rate of 2% per year, expressions involving exponents help determine the future value of your investment. Similarly, in physics, calculating the remaining amount of a radioactive substance after a certain number of half-lives involves exponential decay. These calculations are essential for financial planning and scientific analysis.
