Calculate each value mentally. (24^2)(0.5^2)

Verified step by step guidance

1. Recognize that the expression (24^2)(0.5^2) involves squaring two numbers: 24 and 0.5.
2. Recall that squaring a number means multiplying the number by itself. So, 24^2 means 24 * 24 and 0.5^2 means 0.5 * 0.5.
3. Calculate 24^2 by multiplying 24 by 24.
4. Calculate 0.5^2 by multiplying 0.5 by 0.5.
5. Multiply the results of 24^2 and 0.5^2 together to get the final result.

Key Concepts

Exponents

Exponents represent repeated multiplication of a number by itself. For example, in the expression 24^2, the exponent 2 indicates that 24 is multiplied by itself (24 * 24). Understanding how to manipulate exponents is crucial for simplifying expressions, especially when multiplying numbers with exponents.

Multiplication of Powers

When multiplying numbers with exponents, the bases can be multiplied together if they are the same. However, in this case, we have different bases (24 and 0.5). The multiplication rule states that you can calculate each part separately and then combine the results, which is essential for solving the given expression.

Fractional Exponents

Fractional exponents represent roots of numbers. For instance, 0.5 can be expressed as 1/2, indicating the square root. Thus, 0.5^2 equals 1/4. Recognizing how to interpret and calculate fractional exponents is important for accurately evaluating expressions involving decimals and fractions.