3^-17/8^-14

Answer 1

To simplify this expression, we can use the rule of exponents which states that a^-n equals 1/a^n.

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

To divide fractions, we multiply the numerator by the reciprocal of the denominator.

So, (1/3^17)/(1/8^14) = (1/3^17) * (8^14/1).

Now, we can simplify the expression further by using the rule (a^m)^n = a^(m*n):

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

To evaluate this expression, we can calculate the numerator and denominator separately:

Numerator: 8^14 = (2^3)^14 = 2^(3*14) = 2^42.

Denominator: 3^17.

Therefore, the simplified expression is:

(8^14) / (3^17) = 2^42 / 3^17.