Question

1) (15*3^13+4*27^5)/(17*9^7) 2) (7*2^78-9*2^77)/16^19 по действиям пожалуйста

Answer 1

1)
$\frac{15 \times {3}^{13} + 4 \times {3}^{15} }{17 \times {3}^{14} } = \\ = \frac{(15 + 4 \times {3}^{2}) \times {3}^{13} }{17 \times {3}^{14} } = \\ = \frac{15 + 4 \times 9}{17 \times 3} = \\ = \frac{15 + 36}{51} = \frac{51}{51} = 1$

2)
$\frac{(2 \times 7 - 9) \times 2 {}^{77} }{ {2}^{76} } = \\ = (14 - 9) \times 2 = 5 \times 2 = 10$
Ответ: 1) 1. 2) 10.

Answer 2

Sure, let's simplify these expressions step by step:

1. (15 * 3^13 + 4 * 27^5) / (17 * 9^7)

Step 1: Calculate the exponents and the powers of numbers:

3^13 = 1,594,323 27^5 = 14,348,907

Step 2: Perform the multiplication and addition inside the parentheses:

15 * 1,594,323 + 4 * 14,348,907

Step 3: Perform the multiplication:

23,914,845 + 57,395,628

Step 4: Add the results:

81,310,473

Step 5: Calculate the denominator:

9^7 = 478,296,9

Step 6: Perform the division:

81,310,473 / 478,296,9 ≈ 169.8234

So, the result of the expression is approximately 169.8234.

2. (7 * 2^78 - 9 * 2^77) / 16^19

Step 1: Calculate the exponents and the powers of numbers:

2^78 = 302,231,454,903,657,293,676,544 2^77 = 151,115,727,451,828,646,838,272

Step 2: Perform the multiplication and subtraction inside the parentheses:

7 * 302,231,454,903,657,293,676,544 - 9 * 151,115,727,451,828,646,838,272

Step 3: Perform the multiplication:

2,115,620,184,325,600,057,736,808 - 1,360,041,546,066,457,821,544,448

Step 4: Subtract the results:

755,578,638,259,142,236,192,360

Step 5: Calculate the denominator:

16^19 = 1,099,511,627,776

Step 6: Perform the division:

755,578,638,259,142,236,192,360 / 1,099,511,627,776 ≈ 686.5477

So, the result of the expression is approximately 686.5477.