3^17/8^14

Answer 1

To calculate this without a calculator, we can simplify the expression first:

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

Now, let's break down the numerator and denominator separately:

Numerator: 3^17 = (3^3)^5 * 3^2 = 27^5 * 9
Denominator: 2^42 = (2^3)^14 = 8^14

So, the expression becomes:

(27^5 * 9) / 8^14

We can simplify 27^5 and 8^14 further:

27^5 = (3^3)^5 = 3^15
8^14 = (2^3)^14 = 2^42

Now the expression becomes:

(3^15 * 9) / 2^42

We can now write the expression fully simplified as:

(3^15 * 9) / 2^42 ≈ 875,803,719,682,656,250,000,000 / 4,398,046,511,104,000,000,000,000,000

We can simplify it further if needed by dividing both the numerator and the denominator by common factors.