Question

27^5 - 27^4 ----------------------- = 9^8 + 9^7 + 9^6 (Все, что после этого ^ знака - это степени

Answer 1

(27⁵  - 27⁴  ) / (9⁸+9⁷+9⁶) =
= ( (3³)⁵ - (3³)⁴ )  /  ( (3²)⁸ + (3²)⁷ +(3²)⁶ ) =
=  (3¹⁵  - 3 ¹² )   /  ( 3¹⁶ +3¹⁴  +3¹²) =
=   [ 3¹² (3³ -1) ]   /     [3¹² (3⁴ +3² +1) ] =
=  (3³ -1)  /  (3⁴+3² +1) =
= (27-1)  /  ( 81 +9+1) =
 = 26/91 = 2/7

Answer 2

To solve the equation, let's simplify both sides separately and then compare them.

On the left side of the equation: 27^5 - 27^4

We can factor out 27^4: 27^4(27 - 1)

Simplifying further: 27^4(26)

On the right side of the equation: 9^8 + 9^7 + 9^6

We can factor out 9^6: 9^6(9^2 + 9 + 1)

Simplifying further: 9^6(81 + 9 + 1) 9^6(91)

Now, let's compare both sides of the equation: 27^4(26) = 9^6(91)

Since the bases (27 and 9) are the same on both sides, we can equate the exponents: 27^4 = 9^6 26 = 91

This equation is not true. Therefore, the original statement "27^5 - 27^4 / 27^4 = 9^8 + 9^7 + 9^6" is false.