3^-17 / 8^-14

Question

Apply the Property of Negative Integer Exponents

Answer 1

When applying the property of negative integer exponents, we can rewrite any negative exponent as the reciprocal of the positive exponent.

So, 3^-17 can be rewritten as 1/3^17, and 8^-14 can be rewritten as 1/8^14.

Therefore, the expression becomes:

(1/3^17) / (1/8^14)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:

(1/3^17) * (8^14/1)

Now, we can simplify:

8^14 = (2^3)^14 = 2^(3*14) = 2^42

So, the expression simplifies to:

(1/3^17) * (2^42/1)

Now, we can multiply the numerators and multiply the denominators:

(1 * 2^42) / (3^17 * 1)

Simplifying further:

2^42 / 3^17