To apply the property of negative integer exponents, we can rewrite the given expression as:
(1 / 3^17) / (1 / 8^14)
When we divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. So, we have:
(1 / 3^17) * (8^14 / 1)
Now, let's simplify each individual term:
1 / 3^17 = 1 / (3 * 3 * 3 * ... * 3 * 3), where there are 17 threes. Since we want positive exponents, we can rewrite this as:
(1 / 3^17) = (3^17)^(-1) = 3^(-17)
Similarly,
8^14 = 8 * 8 * 8 * ... * 8 * 8 = (2 * 2 * 2)^14 = 2^(14 * 3) = 2^42
Now, let's substitute these values back into the expression:
(1 / 3^17) * (8^14 / 1) = 3^(-17) * (2^42 / 1)
Since we want positive exponents only, we can rewrite this as:
3^(-17) * (2^42 / 1) = (1 / 3^17) * (2^42 / 1) = 2^42 / 3^17
Therefore, the expression with positive exponents that is equivalent to 3^-17/8^-14 is 2^42 / 3^17.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
3^17/8^-14
1 answer
1 answer