Simplify 5^0/5^-6*1/5^-11/(5^2)^4/(5^10)^2

Answer 1

Looking at this gave me a headache, but I think I composed it correctly:

5⁰/5^-6 * 1/5^-11 / (5²)⁴ / (5¹⁰)²

When we divide by a negative exponent, we flip it to multiply and remove the negative sign. And when we have exponents around parentheses {(5²)⁴ becomes 5⁸}, we multiply them. And when we have an exponent of 0, the coefficient becomes 1:

1 * 5⁶ * 1 * 5¹¹ / 5⁸ / 5²⁰

Anything times 1 is itself:

5⁶ * 5¹¹ / 5⁸ / 5²⁰

So now we add/subtract the exponents:

6 + 11 - 8 - 20 → 17 - 28 = -11

So the final answer is going to be 5^-11 or 1/5¹¹