Find the numerical equivalent of 25 ⋅2−2 (1 point) Responses 128 128 16 16 8 8 2
The numerical equivalent of 25 ⋅2−2 is 8.
To find the numerical equivalent of 25 ⋅ 2^(-2), follow these steps:
1. Calculate 2^(-2):
2^(-2) = 1 / 2^2 = 1 / 4 = 0.25
2. Multiply 25 by 0.25:
25 ⋅ 0.25 = 6.25
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.
To find the numerical value of the expression 25 ⋅ 2^(-2), we can follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to solve it step by step.
Step 1: Calculate the exponent. In this case, we have 2^(-2). To evaluate this, we remember that a negative exponent means we take the reciprocal (or flip) of the base raised to the positive exponent. So, 2^(-2) is equal to 1/2^2.
Step 2: Simplify 2^2. 2^2 is equal to 2 multiplied by itself, which is 4.
Step 3: Divide 1 by 4. So, 1/4 is the result.
Step 4: Multiply 25 by 1/4. Multiplying 25 by 1/4 gives us 25/4.
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 25/4 or 6.25.
Looking at the answer options you provided:
- 128 and 16 are not correct calculations for this expression.
- 8 is also not the correct calculation as it does not account for the division.
- The correct answer is 6.25, which is not one of the answer options you provided.
Therefore, the provided answer options do not include the correct numerical equivalent for 25 ⋅ 2^(-2).