Question

Simplify (x^-9×x^2)^2/(x^3×x^4)^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify this expression, we can use the rules of exponents.

First, let's simplify the numerator:
(x^-9 × x^2)^2 = (x^-7)^2 = x^-14

Next, let's simplify the denominator:
(x^3 × x^4)^3 = (x^7)^3 = x^21

Now, we can simplify the entire expression:
(x^-9 × x^2)^2/(x^3 × x^4)^3 = x^-14/x^21

Using the rule of subtracting exponents when dividing, we can simplify further:
x^-14/x^21 = x^(-14-21) = x^-35

So, the simplified expression is x^-35.

Answer 2

Fully simplify (2^2×2^-6)^-3×(2)^0

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's simplify each part of the expression step by step.

First, let's simplify the term (2^2 × 2^-6)^-3:

(2^2 × 2^-6)^-3 = (4 × 1/2^6)^-3
= (4 × 1/64)^-3
= (4/64)^-3
= (1/16)^-3

Since the exponent is negative, we can rewrite it as the reciprocal with a positive exponent:

(1/16)^-3 = (16/1)^3
= 16^3
= 4096

Now, let's simplify (2)^0:

(2)^0 = 1

Therefore, the fully simplified expression is 4096 × 1 = 4096.

Answer 4

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

To simplify the expression, let's break it down step-by-step:

Step 1: Apply the power of a power rule.
(x^-9 × x^2)^2 = x^-18 × x^4

Step 2: Apply the power of a quotient rule.
(x^3 × x^4)^3 = x^12 × x^12 = x^24

Step 3: Simplify the expression by dividing the two results:
(x^-18 × x^4)/(x^24)

Step 4: Apply the division rule by subtracting the powers of x:
x^-18+4/x^24 = x^-14/x^24

Step 5: Simplify further by subtracting the powers of x:
x^(-14-24) = x^-38

Therefore, the simplified expression is x^-38.