Question

Знайти значення виразу 2^21*27^3+15*4^10*9^4/6^9*2^10+12^10

Answer 1

Пошаговое объяснение:

$\frac{2^{21}*27^{3}+15*4^{10}*9^{4} }{6^{9}*2^{10}+12^{10} } = \frac{2^{21}*(3^{3})^{3} +5*3*(2^{2})^{10} *(3^{2})^{4} }{(2*3)^{9}*2^{10}+(3*2^{2})^{10} } = \frac{2^{21}*3^{9}+5*2^{20}*3^{9} }{2^{9}*3^{9}*2^{10}+3^{10} *2^{20} } =\frac{2^{20}*3^{9}*(2+5) }{2^{19}*3^{9}+3^{10}*2^{20} } = \frac{2^{20}*3^{9}*7 }{2^{19}*3^{9}+3^{10}*2^{20} } = \frac{2^{20}*3^{9}*7 }{2^{19}*3^{9}(1+3*2) }= \frac{2^{20}*3^{9}*7 }{2^{19}*3^{9}*7 }= 2$

Answer 2

To find the value of the expression, follow the order of operations (PEMDAS/BODMAS):

1. Calculate the exponents:

   • 2^21 = 2 raised to the power of 21
   • 27^3 = 27 raised to the power of 3
   • 4^10 = 4 raised to the power of 10
   • 9^4 = 9 raised to the power of 4
   • 6^9 = 6 raised to the power of 9
   • 2^10 = 2 raised to the power of 10
   • 12^10 = 12 raised to the power of 10

2. Perform the multiplication and division:

Now, let's calculate each part separately:

1. 2^21 * 27^3 = (2^21) * (27^3) = 2097152 * 19683 = 41,180,575,616

2. 15 * 4^10 * 9^4 = 15 * (4^10) * (9^4) = 15 * 1048576 * 6561 = 102,642,483,440

3. 6^9 * 2^10 = (6^9) * (2^10) = 10,077,696 * 1024 = 10,334,836,224

4. Add and subtract the results:

Now, let's put everything together:

Expression = 2^21 * 27^3 + 15 * 4^10 * 9^4 / 6^9 * 2^10 + 12^10

Expression = 41,180,575,616 + 102,642,483,440 / 10,334,836,224 + 12^10

Expression = 41,180,575,616 + 9.93609625 + 61917364224

Expression = 41,180,575,625.93609625

The value of the expression is approximately 41,180,575,625.94