Question

Fully simplify
(y^8\cdoty^8)^5/(y^4\cdoty^3)^2

Answer 1

To simplify the expression, we can use the properties of exponents to combine the terms with the same bases.

First, let's simplify the numerator:
(y^8 * y^8)^5 = y^(8*5) * y^(8*5) = y^40 * y^40 = y^(40+40) = y^80

Now, let's simplify the denominator:
(y^4 * y^3)^2 = y^(4*2) * y^(3*2) = y^8 * y^6 = y^(8+6) = y^14

So, the simplified expression is:
(y^8 * y^8)^5 / (y^4 * y^3)^2 = y^80 / y^14

To divide with the same base, we subtract the exponents:
y^80 / y^14 = y^(80-14) = y^66

Therefore, the fully simplified expression is y^66.