Find the numerical equivalent of 25 ⋅2−2 (1 point)
Responses
16
16
8
8
2
2
128
To find the numerical equivalent of 25 ⋅ 2^(-2), we need to apply the order of operations, which states that calculations inside parentheses should be performed first, followed by exponents, multiplication, and division (from left to right), and finally addition and subtraction (from left to right).
In this case, we have an exponent, 2^(-2), and multiplication, 25 ⋅ 2^(-2).
First, let's calculate the exponent:
2^(-2) means raising 2 to the power of -2. When a number is raised to a negative exponent, it is equivalent to 1 divided by the number raised to the positive exponent. So, 2^(-2) is equal to 1 / (2^2), or 1/4.
Now we can substitute this value back into our original expression:
25 ⋅ 1/4
Multiplying a number by a fraction is equivalent to multiplying the number by the numerator and dividing the result by the denominator. So, we can rewrite the expression as:
25 * 1 / 4 = (25 * 1) / 4 = 25 / 4
Now we have a division operation. Dividing 25 by 4 gives us a quotient of 6 with a remainder of 1, which means 25 / 4 = 6.25.
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 6.25.
From the given options, none of them match the correct answer.