Final answer:
we can simplify the given expression: ((2x⁻⁹y⁻¹z⁻⁴)/(4xy⁻³z⁻⁷))⁻¹ to a form with only positive exponents, the simplified form is x¹⁰/ (y²z³).
Step-by-step explanation:
To simplify the expression ((2x⁻⁹y⁻¹z⁻⁴)/(4xy⁻³)z⁻⁷)⁻¹ and write the answer using only positive exponents, we need to understand how to manipulate exponents. When dealing with exponents, there are several rules and properties such as the division property, product property and the negative exponent rule.
To start simplifying, we first cancel out the terms that appear in both the numerator and denominator. Then, we inverse the fraction which simply moves items from the numerator to the denominator and vice versa, where each item changes the sign of its exponent. With that, let's start simplifying.
Step 1: Cancel 2 with the 4 in the denominator, so we get 2 in the denominator. Also, we can subtract the powers of like terms, which means, for 'x', it will be -9 - 1 (as it moved from the denominator to the numerator), giving -10.
Step 2: The 'y' terms become y⁻¹ - -3 = y². And for 'z', we get z⁻⁴ - -7 = z³.
Finally, invert the answer to make all exponents positive, and we get (2x¹⁰)/ (2y²z³). 2's from numerator and denominator cancel out leading to a simplified expression: x¹⁰/ (y²z³).
Learn more about simplifying exponents