Question

Вычислите : 16^3/2-(1/9)^-1/2+27^2/3

Answer 1

16^3/2 - 3 +27^2/3 =  8 *256 - 3 +9*27 = 2048-3+243=2288

Answer 2

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

P - Parentheses/Brackets E - Exponents/Orders MD - Multiplication and Division (from left to right) AS - Addition and Subtraction (from left to right)

Let's break down the expression step-by-step:

1. Calculate the exponents: 16^3 = 16 * 16 * 16 = 4096 (since 16 raised to the power of 3 means 16 multiplied by itself 3 times) (1/9)^(-1/2) = 1 / √(1/9) = 1 / (1/3) = 3 (since the square root of 1/9 is 1/3, and raising it to -1 means taking its reciprocal)

2. Now, the expression becomes: 4096/2 - 3 + 27^(2/3)

3. Calculate division and multiplication (from left to right): 4096/2 = 2048 (since 4096 divided by 2 is 2048)

4. The expression now becomes: 2048 - 3 + 27^(2/3)

5. Calculate 27^(2/3): 27^(2/3) = ∛(27^2) = ∛(729) = 9 (since the cube root of 27^2 is 9)

6. Now, the expression becomes: 2048 - 3 + 9

7. Finally, perform addition and subtraction: 2048 - 3 + 9 = 2054

So, the value of the expression is 2054.