-(4/3)^2+(4/3)^0+4/3-(-4/3)^2+|-(4/3)^2|
( 4 / 3 ) ^ 2 = 16 / 9
- ( 4 / 3 ) ^ 2 = - 16 / 9
( 4 / 3 ) ^ 0 = 1
( - 4 / 3 ) ^ 2 = 16 / 9
- ( - 4 / 3 ) ^ 2 = 16 / 9
( 4 / 3 ) ^ 2 = 16 / 9
- ( 4 / 3 ) ^ 2 = - 16 / 9
abs ( - 16 / 9 ) = 16 / 9
-( 4 / 3 ) ^ 2 + ( 4 / 3 ) ^ 0 + 4 / 3 -( -4 / 3 ) ^ 2 +abs ( - (4 / 3 ) ^ 2 ) =
- 16 / 9 + 1 + 4 / 3 - 16 / 9 + 16 / 9 =
- 16 / 9 + 1 + 4 / 3 =
- 16 / 9 + 9 / 9 + 4 * 3 / ( 3 * 3 ) =
- 16 / 9 + 9 / 9 + 12 / 9 = 5 / 9
Thank you
To simplify the expression -(4/3)^2 + (4/3)^0 + 4/3 - (-4/3)^2 + |-(4/3)^2|, we need to follow the rules of arithmetic operations. Let's break it down step by step:
Step 1: Simplify any exponentiation first.
-(4/3)^2 = -(16/9)
(4/3)^0 = 1
(-4/3)^2 = (16/9)
Step 2: Evaluate the absolute value.
|-(4/3)^2| = |-(16/9)| = (16/9)
Now, let's substitute the simplified expressions back into the original equation:
-(16/9) + 1 + 4/3 - (16/9) + (16/9)
Step 3: Combine like terms within parentheses.
-(16/9) + (16/9) = 0
The expression simplifies to:
0 + 1 + 4/3 + 0 + (16/9)
Step 4: Add the remaining terms together.
0 + 1 + 4/3 + 0 + (16/9) = 1 + 4/3 + 16/9
To simplify this further, we need to find a common denominator for 3 and 9. The least common denominator is 9:
1 + (4/3)*(3/3) + (16/9)
1 + 12/9 + 16/9
Step 5: Add the fractions together.
1 + (12/9) + (16/9) = 1 + (12 + 16)/9 = 1 + 28/9
Step 6: Express the mixed number as an improper fraction.
1 + 28/9 = 9/9 + 28/9 = 37/9
Therefore, -(4/3)^2 + (4/3)^0 + 4/3 - (-4/3)^2 + |-(4/3)^2| simplifies to 37/9.