%2F(4))%5E(3)-((-5)%2F(2))%5E(3)-times(-(2)%2F(3))%5E(4).jpeg "((-3)/(4))^(3)-((-5)/(2))^(3) Times(-(2)/(3))^(4)")
Simplifying the Expression: ((-3)/(4))^(3)-((-5)/(2))^(3) times(-(2)/(3))^(4)
This article will guide you through simplifying the expression: ((−3)/(4))^(3)−((−5)/(2))^(3) times (−(2)/(3))^(4)
Breaking Down the Expression
Let's break down the expression into smaller parts:
- ((−3)/(4))^(3): This means we need to cube the fraction (-3/4). This involves multiplying (-3/4) by itself three times.
- ((−5)/(2))^(3): Similar to the first part, we cube the fraction (-5/2).
- (−(2)/(3))^(4): Here we raise the fraction (-2/3) to the power of four.
Calculating the Powers
Now, let's calculate the individual powers:
- ((−3)/(4))^(3) = (-3/4) * (-3/4) * (-3/4) = -27/64
- ((−5)/(2))^(3) = (-5/2) * (-5/2) * (-5/2) = -125/8
- (−(2)/(3))^(4) = (-2/3) * (-2/3) * (-2/3) * (-2/3) = 16/81
Putting it Together
Now we have: (-27/64) - (-125/8) * (16/81)
To simplify this, we perform the multiplication first:
(-27/64) - (-2000/648)
Finally, we find the common denominator and subtract:
(-216/5184) - (-15625/5184) = 15409/5184
Final Result
Therefore, the simplified value of ((−3)/(4))^(3)−((−5)/(2))^(3) times (−(2)/(3))^(4) is 15409/5184. This fraction can be further simplified by finding the greatest common factor and reducing the terms.