apply the property of negative integer exponents to generate an expression equivalent to 3^-17 over 8^-14 with positive exponents only.
To apply the property of negative integer exponents, we can flip the fractions and change the sign of the exponents.
Therefore, 3^-17 over 8^-14 is equivalent to
(1/3^17) / (1/8^14)
Now, to make the exponents positive, we can rewrite the expression as:
(8^14) / (3^17)
Therefore, the expression equivalent to 3^-17 over 8^-14 with positive exponents only is (8^14) / (3^17).
To apply the property of negative integer exponents, we can rewrite the expression using positive exponents:
3^-17 over 8^-14
The property states that any number raised to a negative exponent can be flipped and changed to a positive exponent. Therefore, we can rewrite the expression as:
(1 / 3^17) / (1 / 8^14)
Now, let's simplify further:
(1 / 3^17) / (1 / 8^14)
= (8^14 / 3^17)
So, the expression equivalent to 3^-17 over 8^-14 with positive exponents only is (8^14 / 3^17).
To apply the property of negative integer exponents, we know that:
a^(-n) = 1 / a^n
Using this property, we can rewrite the given expression 3^(-17) / 8^(-14) as follows:
3^(-17) / 8^(-14) = (1 / 3^17) / (1 / 8^14)
Now, let's simplify each part separately:
1 / 3^17: We can rewrite this expression with a positive exponent by applying the property of negative exponents again:
1 / 3^17 = 3^(-17) = 1 / 3^17
Since 3^(-17) is already in a form with a positive exponent, we don't need to make any further changes.
Similarly, let's simplify 1 / 8^14:
1 / 8^14 = 8^(-14) = 1 / 8^14
Again, we see that 8^(-14) is already in the form with a positive exponent.
Since both expressions, 1 / 3^17 and 1 / 8^14, are already in the positive exponent form, the simplified expression becomes:
(1 / 3^17) / (1 / 8^14) = 3^17 / 8^14
Therefore, the expression equivalent to 3^(-17) / 8^(-14) with positive exponents only is 3^17 / 8^14.