Question

1) 5*2^13*4^11-16^9/(3*2^11)^3

Answer 1

Ответ:

$\frac{5*2^{13}*4^{11}-16^{9}}{3^{3} *2^{33} }$

Answer 2

To solve this expression, follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).

Here's the step-by-step calculation:

1. Calculate the exponents:

   • $2^{13} = 8192$
   • $4^{11} = 4194304$
   • $16^9 = 101559956668416$
   • $(3 \cdot 2^{11})^3 = 5038848^3 = 127783497448693862912$

2. Perform multiplication and division:

   • $5 \cdot 8192 \cdot 4194304 - \frac{101559956668416}{127783497448693862912}$

3. Perform the division:

   • $\frac{101559956668416}{127783497448693862912} \approx 7.9445386 \times 10^{-7}$

4. Multiply:

   • $5 \cdot 8192 \cdot 4194304 - 7.9445386 \times 10^{-7}$

5. Perform the multiplications:

   • $1698693120 - 7.9445386 \times 10^{-7}$

6. Subtract:

   • $1698693120 - 0.00000079445386$

7. Final result:

   • $1698693119.99999920554614$

So, $5 \cdot 2^{13} \cdot 4^{11} - \frac{16^9}{(3 \cdot 2^{11})^3} \approx 1698693119.99999920554614$.