Fully simplify using only positive exponents.

Question

21 xy
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8x^8 y^2

Answer 1

To fully simplify the given expression, 21xy / (8x^8y^2), we need to combine like terms in the numerator and denominator.

In the numerator, we have 21xy, which cannot be simplified further.

In the denominator, we have 8x^8y^2. We can simplify this by separating the variables and combining like terms:

8 * (x^8/x) * (y^2/y)

The term x^8/x is equivalent to x^(8-1), which simplifies to x^7. Similarly, y^2/y simplifies to y^(2-1), which is y^1 or simply y. Therefore, we can simplify the denominator to 8x^7y.

Now, we can rewrite the expression as:

21xy / 8x^7y

Since we have the same variables in the numerator and denominator, we can cancel out the common factors:

21/8 * (xy / x^7y)

Simplifying further, we can cancel out one x and one y:

21/8 * (1 / x^6)

Therefore, the fully simplified expression is:

21/8x^6

Answer 2

INCORRECT

Answer 3

Apologies for the mistake. Let's correct it.

To fully simplify the expression 21xy / (8x^8y^2), we need to combine like terms and simplify the exponents in the denominator.

The numerator, 21xy, cannot be simplified further.

In the denominator, we have 8x^8y^2.

Simplifying the exponents:

x^8 / x^8 simplifies to 1 (x^(8-8) = x^0 = 1).
y^2 / y^2 simplifies to 1 (y^(2-2) = y^0 = 1).

Therefore, the denominator becomes 8 * 1 * 1 = 8.

Now we can rewrite the expression as:

21xy / 8

Since there are no common factors between the numerator and denominator, the expression is fully simplified as:

21xy / 8