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
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.
To apply the property of negative integer exponents in order to generate an expression with positive exponents only, we can reciprocate the terms with negative exponents and change the sign of the exponent. So, for the expression 3^-17/8^-14, we can rewrite it as follows:
3^-17/8^-14 = 8^14/3^17
Now we have the equivalent expression with positive exponents only.
To apply the Property of Negative Integer Exponents and generate an expression with positive exponents only, you need to switch the negative exponents to positive by taking the reciprocal of the base raised to the positive exponent.
Starting with the expression: 3^-17/8^-14
To convert the negative exponent of 3, we can take the reciprocal of 3 and change the exponent to positive:
1/(3^17)
To convert the negative exponent of 8, we'll take the reciprocal of 8 and change the exponent to positive:
1/(1/8^14)
Now we can simplify the expression by multiplying the reciprocals of the base raised to the positive exponent:
1 * 1/(3^17) * 8^14
Simplifying further, we have:
8^14/(3^17)
Therefore, the expression equivalent to 3^-17/8^-14 with positive exponents only is 8^14/(3^17).