Question

What is the value of the quantity (-1/2)�� raised to the power of -3?

1) -512
2) -1
3) 1
4) 512

Answer 1

The value of (-1/2)² raised to the power of -3 is 64.

Step-by-step explanation:

The value of the quantity (-1/2)² raised to the power of -3 can be calculated step by step as follows:

First, evaluate (-1/2)² by squaring the numerator and denominator separately. This gives you 1/4.

Next, raise 1/4 to the power of -3 by taking the reciprocal of 1/4 and cubing it. The reciprocal of 1/4 is 4/1, and cubing 4/1 gives you 64/1.

Therefore, the value of (-1/2)² raised to the power of -3 is 64/1, which simplifies to 64.

Answer 2

The value of the quantity
`\((-1/2)^(-3)\)` is (-8).

To calculate this expression, we need to follow the rules of exponentiation. When a negative base is raised to a negative exponent, it becomes the reciprocal of the base raised to the positive exponent. In this case, \((-1/2)^{-3}\) can be rewritten as
`\((-1/2)^(3)\)`, which is equal to (-1/8). Therefore, the final answer is (-8).

Step-by-step explanation:

The given expression
`\((-1/2)^(-3)\)` involves a negative base raised to a negative exponent. According to the rules of exponentiation, when a negative base is raised to a negative exponent, it becomes the reciprocal of the base raised to the positive exponent. Therefore,
`\((-1/2)^(-3)\) is equivalent to \((-1/2)^(3)`.

Now,
`\((-1/2)^(3)\)` means multiplying (-1/2) by itself three times.
`\((-1/2) * (-1/2) * (-1/2)\) equals \(-1/8\).` Thus, the final value of the expression is (-8).

Exponentiation rules and properties, especially those involving negative bases and exponents. Understanding these rules is crucial for simplifying and evaluating expressions involving exponents.