apply the property of negative integer exponents to generate an expression equivalate to 3-27/8-14

Answer 1

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

The given expression is 3^(-27) / 8^(-14).

To apply the property, we can rewrite it as (1/3)^(27) / (1/8)^(14).

Now, let's simplify these fractions:

(1/3)^(27) = 1^27 / 3^27 = 1 / 3^27
(1/8)^(14) = 1^14 / 8^14 = 1 / 8^14

Putting these simplified fractions back into the expression, we have:

1 / 3^27 / 1 / 8^14

Now, division of fractions can be simplified by multiplying the numerator of the first fraction with the denominator of the second fraction, and the denominator of the first fraction with the numerator of the second fraction:

(1 / 3^27) * (8^14 / 1)

Simplifying this further:

8^14 / 3^27