Evaluate:
(a) 17³
(b) (-21/2)²
(c) (-3)⁵
(d) 2⁸
(e) (-3)⁵ × 5²
(f) (-5) × 10⁴
(g) (-6)³ × (-1)²¹
(h) 2⁷ / 8
(i) 3125 / 243
(j) (2/3)² × (-3/5)³ × (-1)¹⁵ × (-1)²⁸ × (1)⁵¹
Answer (2)
(a) To evaluate 1 7 3 :
1 7 3 = 17 × 17 × 17 = 4913
(b) To evaluate ( − 2 21 ) 2 :
( − 2 21 ) 2 = ( 2 21 ) 2 = 4 441 = 110.25
(c) To evaluate ( − 3 ) 5 :
( − 3 ) 5 = ( − 3 ) × ( − 3 ) × ( − 3 ) × ( − 3 ) × ( − 3 ) = − 243
(d) To evaluate 2 8 :
2 8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
(e) To evaluate ( − 3 ) 5 × 5 2 :
First, calculate ( − 3 ) 5 :
( − 3 ) 5 = − 243
Then calculate 5 2 :
5 2 = 25
Multiply these results: ( − 3 ) 5 × 5 2 = − 243 × 25 = − 6075
(f) To evaluate ( − 5 ) × 1 0 4 :
( − 5 ) × 1 0 4 = − 5 × 10000 = − 50000
(g) To evaluate ( − 6 ) 3 × ( − 1 ) 21 :
First, calculate ( − 6 ) 3 :
( − 6 ) 3 = ( − 6 ) × ( − 6 ) × ( − 6 ) = − 216
Then evaluate ( − 1 ) 21 :
Since the exponent is odd, ( − 1 ) 21 = − 1 .
Multiply these results: ( − 6 ) 3 × ( − 1 ) 21 = − 216 × − 1 = 216
(h) To evaluate 8 2 7 :
First, find 2 7 :
2 7 = 128
Then divide: 8 128 = 16
(i) To evaluate 243 3125 :
As 3125 and 243 do not share common factors other than 1, we just simplify the fraction as is: 243 3125
(j) To evaluate ( 3 2 ) 2 × ( − 5 3 ) 3 × ( − 1 ) 15 × ( − 1 ) 28 × ( 1 ) 51 :
First, calculate each component: ( 3 2 ) 2 = 9 4 ( − 5 3 ) 3 = 125 − 27 ( − 1 ) 15 = − 1 ( − 1 ) 28 = 1 ( 1 ) 51 = 1
Multiply these results: 9 4 × 125 − 27 × − 1 × 1 × 1 = 9 × 125 4 × ( − 27 ) × − 1 = 1125 108
Simplify 1125 108 if possible, or we can leave it as is. This is the final answer.
The evaluations of the expressions yield specific numerical results for each item, such as 1 7 3 = 4913 and ( − 5 ) × 1 0 4 = − 50000 . Each calculation follows standard arithmetic and exponent rules, demonstrating clear steps. The results for each part are systematically derived for clarity and understanding.
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