(y^2)^-4y^8 simplify

y^2 - 4y^8 = y^2 - (2y^4)^2

= (y + 2y^4)(y - 2y^4)

formulas a^2 - b^2 = (a + b)(a - b)

Or, seeing that the expression as written is meaningless, and assuming the usual carelessness with parentheses,

(y^2)^(-4) * y^8
= y^(2 * -4) * y^8
= y^(-8) * y^8
= y^(-8+8)
= y^0
= 1

To simplify the expression (y^2)^-4y^8, we can apply the properties of exponents.

Step 1: Simplify the exponent of (y^2)^-4
The exponent -4 means we need to take the reciprocal of the base and apply the positive exponent. Therefore, (y^2)^-4 becomes (1 / y^2)^4.

Step 2: Simplify the inside of the parenthesis
When we raise a fraction to a power, we raise both the numerator and denominator to that power. Therefore, (1 / y^2)^4 becomes 1^4 / y^(2*4), which is 1 / y^8.

Step 3: Multiply the exponent outside the parentheses
Next, we multiply the exponent outside the parentheses, which is y^8. Therefore, we have (1 / y^8) * y^8.

Step 4: Simplify the expression
Multiplying the expression (1 / y^8) * y^8 gives us 1.

Therefore, the simplified form of (y^2)^-4y^8 is 1.