Calculate each value mentally. (24²)(0.5²)

Verified step by step guidance

1. First, recognize that the expression is a product of two squares: \((24^2)(0.5^2)\).
2. Rewrite the expression using the property of exponents: \((24 imes 0.5)^2\).
3. Calculate the product inside the parentheses: \$24 \times 0.5$.
4. Square the result obtained from the previous step to find the final value.
5. Combine all steps mentally to arrive at the answer without writing intermediate calculations.

Key Concepts

Exponentiation

Exponentiation is the process of raising a base number to a power, indicating how many times the base is multiplied by itself. For example, 24^2 means 24 multiplied by 24. Understanding this helps in calculating powers quickly.

Multiplication of Powers

When multiplying two numbers raised to powers, you calculate each power separately and then multiply the results. For instance, (24^2)(0.5^2) means find 24 squared and 0.5 squared, then multiply those two values.

Mental Math Strategies

Mental math involves performing calculations quickly without paper. Recognizing squares of common numbers and decimals, like 24^2 = 576 and 0.5^2 = 0.25, allows for efficient computation of the product mentally.