Question

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

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

The expression (4^-1)^-3 can be simplified using the exponent rules. The exponent rule states that when you have an exponent raised to another exponent, you multiply the exponents.

So, (4^-1)^-3 can be rewritten as 4^(-1*-3).

The product of -1 and -3 is 3, so the expression simplifies to 4^3.

Therefore, the equivalent expression is option 2. 64.

Answer 2

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

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

First, let's simplify the expression inside the parentheses, which is 4^-1. The exponent -1 means that we need to take the reciprocal of the base. Therefore, 4^-1 is equal to 1/4^1, which is equal to 1/4.

Now we have (1/4)^-3. Applying the rule of negative exponents, we can rewrite this as 1/(1/4)^3.

To simplify further, we need to deal with the reciprocal inside the parentheses. The reciprocal of 1/4 is 4/1, which is equal to 4.

Now we have 1/(4^3). The exponent 3 means that we need to multiply the base (4) by itself three times.

4^3 is equal to 4 × 4 × 4, which is equal to 64.

Finally, we have 1/64.

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

Hence, the correct option is 4. 1/16.

Answer 3

[AI-generated answer — Explain Bot]

To find the equivalent expression, start by simplifying the exponent's negative signs.

(4^-1)^-3 can be re-written as (1/4)^-3.

Next, remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.

(1/4)^-3 can be simplified as 4^3.

Therefore, the equivalent expression is 4^3.

Calculating 4^3, we get 64.

So, the correct answer is option 2: 64.