11/16-(-3/4)^2 divided by 2/5 ^3
[11/16 - 9/16]/(8/125)
= (2/16)/(8/125)
= 125
To simplify the expression 11/16-(-3/4)^2 divided by 2/5^3, we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
Step 1: Evaluate the exponent in parentheses.
(-3/4)^2 means raising -3/4 to the power of 2.
To find the power of a fraction, we need to square both the numerator and the denominator separately. So, we have:
(-3/4)^2 = (-3)^2 / (4)^2 = 9/16
Now our expression becomes 11/16 - 9/16 divided by 2/5^3.
Step 2: Simplify the division involving exponent.
Recall that to divide fractions, we need to multiply by the reciprocal of the denominator. So, we have:
2/5^3 = 2/(5^3) = 2/125
Now our expression becomes 11/16 - 9/16 divided by 2/125.
Step 3: Perform the division.
To divide fractions, we need to multiply by the reciprocal of the second fraction. So, we have:
(9/16) ÷ (2/125) = (9/16) * (125/2)
Now our expression becomes 11/16 - (9/16) * (125/2).
Step 4: Simplify the remaining multiplication and subtraction.
Multiply the numerators together and the denominators together:
(9/16) * (125/2) = (9 * 125) / (16 * 2) = 1125/32
Now our expression becomes 11/16 - 1125/32.
Step 5: Find a common denominator and subtract the fractions.
Since the denominators are not the same, we need to find a common denominator. In this case, the lowest common multiple of 16 and 32 is 32. So, we need to convert 11/16 into an equivalent fraction with a denominator of 32:
11/16 = (11/16) * (2/2) = 22/32
Now the expression becomes 22/32 - 1125/32.
Subtract the numerators and keep the common denominator:
(22 - 1125) / 32 = -1103/32
Therefore, the simplified form of the expression 11/16-(-3/4)^2 divided by 2/5^3 is -1103/32.