3^-17/8^-14=

Answer 1

To solve this expression, we can apply the exponent property that states when dividing two numbers with the same base, we subtract the exponents.

Therefore, 3^-17/8^-14 can be rewritten as:

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

Now we can simplify further by calculating the value inside the parentheses:

3/8 = (2 * 3)/(2 * 4) = (1/2) * (3/4) = 3/8

So the expression becomes:

(3/8)^(-17) * 8^14 = (3/8)^(-17) * 2^14 * 2^14

Now we can apply the exponent property that states when raising a number to a negative exponent, we flip the base and make the exponent positive.

Therefore:

(3/8)^(-17) = (8/3)^17

So the expression simplifies to:

(8/3)^17 * 2^14 * 2^14

Now we can multiply the exponents of 2 to simplify further:

2^(14+14) = 2^28

Finally, the expression becomes:

(8/3)^17 * 2^28