apply the property of negative integer exponent to generate an expression equivalent to 3 to the power of -17 divided by 8 to the power of -14 with positive exponents only

Answer 1

To apply the property of negative integer exponent, we can rewrite the expression by moving the negative exponents to the denominator and changing their signs.

The expression 3^(-17) divided by 8^(-14) is equivalent to (1/3^17) divided by (1/8^14).

To convert the negative exponent to positive, we take the reciprocal of the base.

So, the expression can be rewritten as (1/(3^17)) divided by (1/(1^14 x 8^14)).

Since any number raised to the power of 1 is equal to the number itself, we can simplify further to get:

1/(3^17) divided by (1/(8^14)).

Finally, when we divide by a fraction, we multiply by the reciprocal of that fraction.

Therefore, the expression is equivalent to (1/(3^17)) times (8^14).

So, the expression with positive exponents only is 8^14 divided by 3^17.