3^-17/8^-14
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.
To simplify the expression 3^-17/8^-14, we can first use the rule of negative exponents which states that a^(-n) is equal to 1/a^n. Applying this rule to the expression, we have:
3^-17/8^-14 = (1/3^17)/(1/8^14)
Next, we can simplify this expression by multiplying the numerator and denominator by the reciprocal of the numerator, which is 8^14:
(1/3^17)/(1/8^14) = (1/3^17)*(8^14/1)
Now, let's multiply the numerators and the denominators:
(1/3^17)*(8^14/1) = (1*8^14)/(3^17*1)
To simplify further, we can rewrite 8^14 as (2^3)^14, and then use the rule of exponents which states that (a^m)^n = a^(m*n):
(1*8^14)/(3^17*1) = (1*(2^3)^14)/(3^17*1)
Simplifying the exponent 14 in (2^3)^14, we have:
(1*2^42)/(3^17*1)
Finally, we have:
3^-17/8^-14 = (1*2^42)/(3^17*1) = 2^42/3^17 as the simplified expression.