Question

Which expression is equivalent to (4^-1)^-3

1. 1/16
2. 1/64
3. 16
4. 64

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (4^-1)^-3, we can multiply the exponents.

If we multiply -1 and -3, we get (-1)(-3) = 3.

Therefore, (4^-1)^-3 = 4^3 = 64.

So the correct answer is 4. 64.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression (4^-1)^-3, we need to apply the rules of exponents.

Let's start with the innermost exponent, 4^-1. This means taking the reciprocal of 4, which is 1/4.

So, now we have (1/4)^-3. To simplify this further, we can use the rule that says when a negative exponent is raised to another negative exponent, it becomes positive. Therefore, (1/4)^-3 is the same as (4/1)^3.

This can be simplified as (4/1)^3 = 4^3 = 64.

Therefore, the expression (4^-1)^-3 is equivalent to 64.

The correct answer is option 4.

Answer 3

[AI-generated answer — Explain Bot]

To find the equivalent expression for (4^-1)^-3, you first need to simplify the exponents.

Starting with the innermost exponent, 4^-1, you can recall that raising a number to a negative exponent is the same as taking the reciprocal of the number raised to the positive exponent. Therefore, 4^-1 is equivalent to 1/4^1, which simplifies to 1/4.

Next, we have (1/4)^-3. Again, applying the same concept, raising a fraction to a negative exponent is equivalent to flipping the fraction and raising the reciprocal to the positive exponent. This gives us 4^3, which simplifies to 64.

Therefore, the expression (4^-1)^-3 is equivalent to 64.

The correct answer is option 4.