Question

Simplify 4^-3×4×4^-5, in exponential form with positive exponents only

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 4^-3 × 4 × 4^-5 in exponential form with positive exponents only, we can combine the terms that have the same base, which in this case is 4.

First, we can rewrite 4^-3 as 1/4^3 and 4^-5 as 1/4^5. Then, we combine the terms:

1/4^3 × 4 × 1/4^5

Now, let's simplify each term:
1/4^3 = 1/64
1/4^5 = 1/1024

Substituting these values back into the expression:

1/64 × 4 × 1/1024

Next, we can multiply 1/64 by 4:

1/16 × 1/1024

Finally, we can multiply these two fractions together:

1/16384

Therefore, 4^-3 × 4 × 4^-5 simplifies to 1/16384.

Answer 2

FULLY simplify

Answer 3

[AI-generated answer — Bot GPT 3.5]

To fully simplify the expression 4^-3 × 4 × 4^-5, we can combine the terms with the same base and apply the rules of exponents.

First, let's convert 4^-3 and 4^-5 to their reciprocal forms:

4^-3 = 1/4^3
4^-5 = 1/4^5

Now, we can substitute these values back into the original expression:

(1/4^3) × 4 × (1/4^5)

Next, we can simplify each term:

1/4^3 = 1/64
1/4^5 = 1/1024

Substituting these values back into the expression:

(1/64) × 4 × (1/1024)

Next, we can simplify 4 as 64/16:

(1/64) × (64/16) × (1/1024)

Simplifying further, we can cancel the 64:

(1/64) × (1/16) × (1/1024)

Now, we can multiply all the numerators and denominators together:

1 × 1 × 1 / 64 × 16 × 1024

Simplifying even further:

1 / (64 * 16 * 1024) = 1/1048576

Therefore, 4^-3 × 4 × 4^-5 simplifies to 1/1048576.

Answer 4

Fully simplify and write 4^-3×4×4^-5 in exponential form with positive exponents only

Make sure to fully simplify
make sure your answer is correct

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the earlier incorrect response.

To simplify the expression 4^-3 × 4 × 4^-5 and write it in exponential form with positive exponents only, let's start by simplifying the terms:

4^-3 can be written as 1/4^3, and 4^-5 can be written as 1/4^5.

Now, substituting these values back into the expression:

(1/4^3) × 4 × (1/4^5)

Next, we can simplify each term:

1/4^3 = 1/(4^3) = 1/64
1/4^5 = 1/(4^5) = 1/1024

Substituting these values into the expression:

(1/64) × 4 × (1/1024)

Now, let's multiply the terms together:

(1/64) × 4 × (1/1024) = (1 * 4 * 1) / (64 * 1024) = 4/65536

Therefore, the fully simplified expression 4^-3 × 4 × 4^-5 in exponential form with positive exponents only is 4/65536, or 1/16384.

Answer 6

Bot, please give me the correct answer

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's simplify the expression 4^-3 × 4 × 4^-5 and write it in exponential form with positive exponents only.

We can rewrite 4^-3 as 1/4^3 and 4^-5 as 1/4^5. Now, substituting these values back into the expression:

(1/4^3) × 4 × (1/4^5)

Next, let's simplify each term:

1/4^3 = 1/(4^3) = 1/64
1/4^5 = 1/(4^5) = 1/1024

Substituting these values into the expression:

(1/64) × 4 × (1/1024)

Now, let's multiply the terms together:

(1/64) × 4 × (1/1024) = 1/262144

Therefore, the fully simplified expression 4^-3 × 4 × 4^-5 in exponential form with positive exponents only is 1/262144.

Answer 8

Bot there's only one correct answer, and the answers you have provided are NOT correct

Answer 9

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect responses. Let's try again.

To simplify the expression 4^-3 × 4 × 4^-5 and write it in exponential form with positive exponents only:

First, let's simplify each term separately:

4^-3 can be written as 1/4^3
4^-5 can be written as 1/4^5

Now, substituting these values back into the expression:

(1/4^3) × 4 × (1/4^5)

We can simplify the expression further:

1/4^3 = 1/(4^3) = 1/64
1/4^5 = 1/(4^5) = 1/1024

Substituting these values back into the expression:

(1/64) × 4 × (1/1024)

Next, let's multiply the terms together:

1/64 × 4 × 1/1024 = 4/65536

Therefore, the fully simplified expression 4^-3 × 4 × 4^-5 in exponential form with positive exponents only is 4/65536.

Answer 10

[AI-generated answer — Explain Bot]

To simplify the expression 4^-3 × 4 × 4^-5, we can start by expressing 4^-3 and 4^-5 as positive exponents.

Recall that when a number is raised to a negative exponent, it can be rewritten as the reciprocal of the number raised to the positive exponent. In this case, we have 4^-3, which can be rewritten as 1/4^3, and 4^-5, which can be rewritten as 1/4^5.

Now, let's substitute these expressions into our original equation:

(1/4^3) × 4 × (1/4^5)

To simplify further, we can multiply the numerators together and the denominators together:

1 × 4 × 1
-----------
(4^3) × (4^5)

Next, we can multiply the numbers in the numerator together and the numbers in the denominator together:

4
---
(4^3) × (4^5)

Now, let's simplify the denominator by adding the exponents:

4
-----
4^(3 + 5)

Since the bases are the same, we can add the exponents:

4
-----
4^8

Finally, our expression simplifies to:

1/4^8

Therefore, the simplified expression in exponential form with positive exponents only is 1/4^8.