2^{-1} \left[ \left(\frac{5}{2}\right)^4 + \left(\frac{3}{5}\right)^{-2} \right] \div \frac{17}{9} =
Answer (1)
Let's solve the expression step-by-step:
Given expression:
2 − 1 [ ( 2 5 ) 4 + ( 5 3 ) − 2 ] ÷ 9 17
Start by evaluating the exponents:
2 − 1 = 2 1
( 2 5 ) 4 = 2 4 5 4 = 16 625
( 5 3 ) − 2 = ( 3 5 ) 2 = 3 2 5 2 = 9 25
Substitute back into the expression:
2 1 [ 16 625 + 9 25 ] ÷ 9 17
Add the fractions inside the brackets. To do this, find a common denominator which is 144:
16 625 = 144 625 × 9 = 144 5625
9 25 = 144 25 × 16 = 144 400
Add them:
144 5625 + 144 400 = 144 6025
Multiply by 2 1 :
2 1 × 144 6025 = 288 6025
Divide by 9 17 :
Dividing by a fraction is the same as multiplying by its reciprocal:
288 6025 × 17 9
Calculate:
288 × 17 6025 × 9
Simplify the fractions if possible:
4896 54225 ≈ 11.08
Therefore, the value of the expression is approximately 11.08 .
