apply the property of negative integer exponents to generate an expression equivalent to 3^-17 / 8 ^-14
To apply the property of negative integer exponents, we can rewrite the expression as:
(8^14 / 3^17)
Let's simplify further:
8^14 = (2^3)^14 = 2^(3*14) = 2^42
3^17 = 3^17
Therefore, the expression simplified using the property of negative integer exponents is:
(2^42 / 3^17)
To apply the property of negative integer exponents, we can rewrite the expression as the reciprocal with positive exponents. Negative exponent property states that a number raised to a negative exponent is equal to 1 divided by the number raised to the positive exponent.
So, 3^-17 / 8^-14 can be rewritten as (1 / 3^17) / (1 / 8^14).
Next, we can simplify it further by multiplying the numerator and denominator by the reciprocal of the denominator:
(1 / 3^17) * (8^14 / 1)
Simplifying further, we get:
8^14 / 3^17
To apply the property of negative integer exponents, we can rewrite the expression in terms of positive exponents. The property states that any number raised to a negative exponent can be written as the reciprocal of the number raised to the positive exponent.
Let's start by rewriting the expression using positive exponents:
3^-17 / 8^-14
To convert 3^-17 to a positive exponent, we take its reciprocal:
1 / 3^17
Similarly, to convert 8^-14 to a positive exponent, we take its reciprocal:
1 / 8^14
Now, let's simplify the rewritten expression:
1 / 3^17 / 1 / 8^14
To divide fractions, we can multiply the numerator by the reciprocal of the denominator:
1 / 3^17 * 8^14 / 1
Applying the power of a product rule, we can combine the exponents:
1 / (3 * 8)^17
Simplifying further:
1 / 24^17
Therefore, the expression equivalent to 3^-17 / 8^-14 is 1 / 24^17.