%2F(3))%5E(4)--(-(1)%2F(3))%5E(8)times(-(1)%2F(3))%5E(5).jpeg "(-(1)/(3))^(4)- (-(1)/(3))^(8)times(-(1)/(3))^(5)")
Solving the Expression: ((-1/3)^(4) - (-1/3)^(8)) × (-1/3)^(5)
In this article, we will solve the given expression: ((-1/3)^(4) - (-1/3)^(8)) × (-1/3)^(5).
Step 1: Simplify the Expression
Let's break down the expression into smaller parts and simplify each component:
(-1/3)^(4) = (-1)^(4) × (1/3)^(4) = 1 × (1/81) = 1/81 (-1/3)^(8) = (-1)^(8) × (1/3)^(8) = 1 × (1/6561) = 1/6561
Now, let's subtract the two expressions:
(-1/3)^(4) - (-1/3)^(8) = 1/81 - 1/6561 = (6561 - 81)/524041 = 5480/524041
Step 2: Multiply by (-1/3)^(5)
Now, let's multiply the result by (-1/3)^(5):
((5480/524041) × (-1/3)^(5) = (5480/524041) × (-1)^(5) × (1/3)^(5) = (-5480/524041) × (1/243) = -5480/12754527
Final Answer
The final solution to the expression is:
(-5480/12754527)
Therefore, the value of the given expression is -5480/12754527.
