Question

(16^-3)^а/6. Если а= -1/2

Answer 1

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Answer 2

To solve the expression (16^-3)^(а/6) when а = -1/2, we can follow these steps:

Step 1: Substitute the value of а into the expression. Step 2: Evaluate the expression.

Let's proceed with the calculations:

Step 1: Substitute the value of а = -1/2

(16^-3)^(а/6) = (16^-3)^((-1/2)/6)

Step 2: Simplify and calculate

First, let's simplify the exponent:

((-1/2)/6) = -1/2 * (1/6) = -1/12

Now, we can calculate the expression:

(16^-3)^((-1/2)/6) = (16^-3)^(-1/12)

To calculate (16^-3)^(-1/12), we can use the fact that a negative exponent is the reciprocal of the positive exponent:

(16^-3)^(-1/12) = 1 / (16^(3*(1/12))) = 1 / (16^(1/4))

Now, we need to calculate 16^(1/4), which is the fourth root of 16:

16^(1/4) = √(√16) = √(4) = 2

Finally, substitute this value back into the expression:

1 / (16^(1/4)) = 1 / 2 = 0.5

So, the final result of the expression (16^-3)^(а/6) when а = -1/2 is 0.5.