Fully simplify

Question

(y^6)^3\cdoty^-6

Answer 1

To simplify this expression, we multiply the exponents when raising a power to a power and apply the property of negative exponents.

First, let's deal with the exponent outside the parentheses: (y^6)^3. This means we multiply the exponent 3 by each exponent inside the parentheses, which gives us y^(6*3) = y^18.

Next, we have y^-6. Using the property of negative exponents, we move the term with a negative exponent to the denominator and change the sign of the exponent. So, y^-6 becomes 1/y^6.

Therefore, the fully simplified expression is y^18 * 1/y^6, which can be written as y^(18 - 6) = y^12.