Question

Hi Regina

Can you simplify (x^8/x^2)^2×(x^8/x^4)^4

The answer is not x^28 can you use some kind of form that makes the answer anything but x^28??

Answer 1

[AI-generated answer — Bot GPT 3.5]

Hi there!

Sure, let's simplify the expression (x^8/x^2)^2 × (x^8/x^4)^4.

First, let's simplify inside the parentheses separately.

(x^8/x^2)^2 simplifies to (x^6)^2 because when dividing with the same base, x^8 divided by x^2 equals x^(8-2) which is x^6.

Therefore, (x^8/x^2)^2 becomes x^(6*2) which is x^12.

Similarly, (x^8/x^4)^4 simplifies to (x^4)^4 because x^8 divided by x^4 equals x^(8-4) which is x^4.

Therefore, (x^8/x^4)^4 becomes x^(4*4) which is x^16.

Now let's simplify the entire expression by multiplying x^12 and x^16.

(x^12) × (x^16) = x^(12+16) = x^28.

So the simplified expression is indeed x^28.

If you're looking for an alternative form apart from x^28, there isn't one in this case. The simplification leads to x^28 as the answer.

Answer 2

Simplify (x^4/x^2)^2×(x^8/x^4)^4

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (x^4/x^2)^2 × (x^8/x^4)^4, we can apply the rules of exponents.

First, inside the parentheses, x^4 divided by x^2 gives us x^(4 - 2) which simplifies to x^2.

Therefore, (x^4/x^2)^2 becomes (x^2)^2 which is x^(2 * 2) or x^4.

Next, inside the second set of parentheses, x^8 divided by x^4 gives us x^(8 - 4) which simplifies to x^4.

Thus, (x^8/x^4)^4 simplifies to (x^4)^4 which is x^(4 * 4) or x^16.

Now let's simplify the entire expression by multiplying x^4 and x^16.

(x^4) × (x^16) = x^(4 + 16) = x^20.

Therefore, the simplified expression is x^20.

Answer 4

SIMPLIFY (z^7)^3\cdotz^2

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (z^7)^3 ⋅ z^2, we can apply the rules of exponents.

First, we know that (z^7)^3 means we raise z^7 to the power of 3, which gives us (z^7)^3 = z^(7*3) or z^21.

Next, we multiply this result by z^2, so we have z^21 ⋅ z^2. Using the rule of multiplication of the same base, we add the exponents, giving us z^(21 + 2) or z^23.

Therefore, the simplified expression is z^23.

Answer 6

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

To simplify the expression (x^8/x^2)^2 × (x^8/x^4)^4, we can follow these steps:

Step 1: Simplify each fraction individually.
(x^8/x^2)^2 = (x^6)^2 = x^12
(x^8/x^4)^4 = (x^4)^4 = x^16

Step 2: Multiply the simplified fractions.
x^12 × x^16 = x^(12+16) = x^28

Therefore, the simplified form of the expression is x^28.

Answer 7

[AI-generated answer — Explain Bot]

Hello!

To simplify the expression (x^8/x^2)^2 × (x^8/x^4)^4, we need to use the rules of exponents.

Let's break it down step by step:

Step 1: Simplify the first term, (x^8/x^2)^2.
To simplify this, we divide the exponents and keep the base the same, so (x^8/x^2)^2 can be written as (x^(8-2))^2 or x^6^2 which is equal to x^12.

Step 2: Simplify the second term, (x^8/x^4)^4.
Similarly, dividing the exponents and keeping the base the same, (x^8/x^4)^4 becomes (x^(8-4))^4 or x^4^4 which is equal to x^16.

Step 3: Now, multiply the simplified terms:
x^12 * x^16 = x^(12+16) = x^28.

As you can see, the simplified answer is x^28, which matches the result you mentioned. However, if you want a different form rather than x^28, you can write it in terms of a positive exponent.

For example, x^28 can also be written as (x^4)^7 or (x^14)^2. These forms are equivalent to x^28 but presented in a different way.

Let me know if there's anything else I can help you with!