Question

(0,5a^-2)^2:(32a^2 b^2)^3 при a=(0,5)^-4 b=0,25

Answer 1

Ответ:

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Объяснение:

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Answer 2

To evaluate the expression $(0.5a^{-2})^2:(32a^2 b^2)^3$ when $a = (0.5)^{-4}$ and $b = 0.25$, follow these steps:

Step 1: Substitute the values of $a$ and $b$ into the expression.

Step 2: Simplify the expression.

Let's start:

Step 1: $a = (0.5)^{-4} = 2^4 = 16$

$b = 0.25$

Step 2: $(0.5a^{-2})^2:(32a^2 b^2)^3$

Substitute the values:

$(0.5(16)^{-2})^2:(32(16)^2(0.25)^2)^3$

Simplify:

$(0.5 \times 16^{-2})^2:(32 \times 16^2 \times 0.25^2)^3$

Calculate the powers:

$(0.5 \times \frac{1}{16^2})^2:(32 \times 16^2 \times 0.25^2)^3$

$(0.5 \times \frac{1}{256})^2:(32 \times 256 \times 0.0625)^3$

$(0.5 \times \frac{1}{256})^2:(8 \times 0.0625)^3$

$(0.5 \times \frac{1}{256})^2:(0.5)^3$

Calculate the remaining expressions:

$(\frac{0.5}{256})^2:(0.5)^3$

$(\frac{0.5}{256})^2:(0.5 \times 0.5 \times 0.5)$

$(\frac{0.5}{256})^2:(\frac{1}{8})$

Now, square $\frac{0.5}{256}$:

$(\frac{1}{512}):(\frac{1}{8})$

Divide by a fraction by multiplying its reciprocal:

$\frac{1}{512} \times \frac{8}{1}$

Simplify the division:

$\frac{8}{512} = \frac{1}{64}$

So, the final result is $\frac{1}{64}$.