Answer:
9.765625×10^6
Step-by-step explanation:
Simplify the following:
5^2×5^9/5
Hint: | Express 5^2×5^9/5 as a single fraction.
5^2×5^9/5 = (5^2×5^9)/5:
(5^2×5^9)/5
Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to (5^2×5^9)/5.
Combine powers. (5^2×5^9)/5 = 5^(9 + 2 - 1):
5^(9 + 2 - 1)
Hint: | Evaluate 9 + 2.
9 + 2 = 11:
5^(11 - 1)
Hint: | Subtract 1 from 11.
| 1 | 1
- | | 1
| 1 | 0:
5^10
Hint: | Compute 5^10 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
5^10 = (5^5)^2 = (5×5^4)^2 = (5 (5^2)^2)^2:
(5 (5^2)^2)^2
Hint: | Evaluate 5^2.
5^2 = 25:
(5×25^2)^2
Hint: | Evaluate 25^2.
| 2 | 5
× | 2 | 5
1 | 2 | 5
5 | 0 | 0
6 | 2 | 5:
(5×625)^2
Hint: | Multiply 5 and 625 together.
5×625 = 3125:
3125^2
Hint: | Evaluate 3125^2.
| | | 3 | 1 | 2 | 5
× | | | 3 | 1 | 2 | 5
| | 1 | 5 | 6 | 2 | 5
| | 6 | 2 | 5 | 0 | 0
| 3 | 1 | 2 | 5 | 0 | 0
9 | 3 | 7 | 5 | 0 | 0 | 0
9 | 7 | 6 | 5 | 6 | 2 | 5:
Answer: | 9765625 = 9.765625×10^6
