(1+3*2^-1)^-2

Suzhoumeite

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Jun 07, 2024

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Evaluating the Expression: (1+3*2^-1)^-2

In this article, we will evaluate the expression (1+3*2^-1)^-2 step by step.

Step 1: Evaluate the inner expression

First, let's evaluate the expression inside the parentheses:

3*2^-1

To evaluate this expression, we need to follow the order of operations (PEMDAS):

• 2^-1 equals 1/2 (since a^-1 is equivalent to 1/a)
• 3*(1/2) equals 3/2

So, the inner expression becomes:

1 + 3/2

Step 2: Simplify the fraction

Now, let's simplify the fraction:

3/2 equals 1.5

So, the expression becomes:

1 + 1.5

Step 3: Evaluate the sum

Now, let's evaluate the sum:

1 + 1.5 equals 2.5

Step 4: Raise to the power of -2

Finally, let's raise 2.5 to the power of -2:

(2.5)^-2 equals 1/(2.5)^2

1/(2.5)^2 equals 1/6.25

Final Answer

The final answer is:

(1+3*2^-1)^-2 equals 1/6.25

There you have it! We have successfully evaluated the expression (1+3*2^-1)^-2 step by step.