Question

4m⁹ n⁻³/ 8n⁻²m⁻¹ Write your answer using only positive exponent

Answer 1

To simplify the expression with positive exponents, divide the coefficients, subtract the exponents for the common bases, and convert any negative exponents into positive by taking the reciprocal. Resulting expression: 1/2m¹⁰n.

Step-by-step explanation:

To simplify the expression 4m⁹ n⁻³ over 8n⁻²m⁻¹ and write it using only positive exponents, we need to follow the rules for dividing powers with the same base. When dividing powers with the same base, we subtract the exponents of the common bases. Additionally, to convert negative exponents into positive exponents, we take the reciprocal of the base.

Let's simplify step by step:

1. Divide coefficients (numerical parts): 4 / 8 = 1/2.
2. Subtract exponents of m: 9 - (-1) = 9 + 1 = 10. So, m will have a positive exponent of 10.
3. Subtract exponents of n: (-3) - (-2) = -3 + 2 = -1. To make the exponent of n positive, we bring it to the numerator as n¹.

Putting it all together, the simplified expression with only positive exponents is 1/2 * m¹⁰ * n¹ or 1/2m¹⁰n.