Fully simplify using only positive exponents 2x^8y^2/8x^8y^7

Answer 1

To simplify the expression fully using only positive exponents, we can use the properties of exponents.

First, let's simplify the numerator: 2x^8y^2.

Since there are no like terms to combine, we simply rewrite the numerator as it is: 2x^8y^2.

Next, let's simplify the denominator: 8x^8y^7.

We can break down 8 into its prime factors: 8 = 2 * 2 * 2.
Similarly, we can break down x^8 into its prime factors: x^8 = x * x * x * x * x * x * x * x.
And we can break down y^7 into its prime factors: y^7 = y * y * y * y * y * y * y.

Now let's simplify the expression by canceling out the common factors between the numerator and denominator:

2x^8y^2 / 8x^8y^7 = (2 * x * x * y * y) / (2 * 2 * 2 * x * x * x * x * x * x * x * y * y * y * y * y * y * y).

Canceling out the common factors:

2x^8y^2 / 8x^8y^7 = (1) / (2 * x * x * x * x * x * y * y * y * y).

Simplifying further:

2x^8y^2 / 8x^8y^7 = 1 / (32x^5y^4).

Therefore, the fully simplified expression is 1 / (32x^5y^4).