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3 years ago

(5^3)^2 . (4^2)^2 . (6^2)^3

Mathematics

1 answer:

Vladimir79 [104]3 years ago

7 0

Answer:

1. 15625

2. 256

3. 46656

Step-by-step explanation:

Simplify the following:

(5^3)^2

Multiply exponents. (5^3)^2 = 5^(3×2):

5^(3×2)

3×2 = 6:

5^6

5^6 = (5^3)^2 = (5×5^2)^2:

(5×5^2)^2

5^2 = 25:

(5×25)^2

5×25 = 125:

125^2

| | 1 | 2 | 5

× | | 1 | 2 | 5

| | 6 | 2 | 5

| 2 | 5 | 0 | 0

1 | 2 | 5 | 0 | 0

1 | 5 | 6 | 2 | 5:

Answer: 15625

_________________________________________

Simplify the following:

(4^2)^2

Multiply exponents. (4^2)^2 = 4^(2×2):

4^(2×2)

2×2 = 4:

4^4

4^4 = (4^2)^2:

(4^2)^2

4^2 = 16:

16^2

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

Answer: 256

____________________________________________

Simplify the following:

(6^2)^3

Multiply exponents. (6^2)^3 = 6^(2×3):

6^(2×3)

2×3 = 6:

6^6

6^6 = (6^3)^2 = (6×6^2)^2:

(6×6^2)^2

6^2 = 36:

(6×36)^2

6×36 = 216:

216^2

| | 2 | 1 | 6

× | | 2 | 1 | 6

| 1 | 2 | 9 | 6

| 2 | 1 | 6 | 0

4 | 3 | 2 | 0 | 0

4 | 6 | 6 | 5 | 6:

Answer: 46656

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