Question

(4^10:4^8)*(6^8:6^6):(24^37:24^36)

Answer 1

Ответ:

Объяснение:

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Answer 2

To simplify the expression (4^10:4^8) * (6^8:6^6) : (24^37:24^36), let's break it down step by step:

(4^10:4^8) means dividing 4 raised to the power of 10 by 4 raised to the power of 8.

4^10 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 1,048,576 4^8 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 65,536

(4^10:4^8) = 1,048,576 / 65,536 = 16

Similarly, (6^8:6^6) means dividing 6 raised to the power of 8 by 6 raised to the power of 6.

6^8 = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1,679,616 6^6 = 6 * 6 * 6 * 6 * 6 * 6 = 46,656

(6^8:6^6) = 1,679,616 / 46,656 = 36

Finally, (24^37:24^36) means dividing 24 raised to the power of 37 by 24 raised to the power of 36.

24^37 = 24 * 24 * 24 * ... * 24 (37 times) 24^36 = 24 * 24 * 24 * ... * 24 (36 times)

When you divide the same base with exponents, you subtract the exponents: 24^37 / 24^36 = 24^(37-36) = 24^1 = 24

Now we can substitute these values back into the original expression:

(16 * 36) : 24

Multiplying 16 by 36 gives us 576:

576 : 24

Dividing 576 by 24:

576 / 24 = 24

Therefore, the simplified expression is 24.