Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.

Answer 1

To apply the property of negative integer exponents, we have to reciprocate the base and change the sign of the exponent.

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

Using these equivalences, the expression 3^(-17)/8^(-14) becomes:

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

When we divide by a fraction, we multiply by its reciprocal. So, we can rewrite the division as multiplication by the reciprocal:

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

Multiplying the numerators and denominators gives us:

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

Simplifying further, we have:

8^14 / 3^17

And that is the expression with positive exponents only.