Question

PLEASE HELP: Simplify the expression. Write your answer as a power. 5^2⋅5^9/5

Answer 1

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