Question

2m⁶n⁴ /(6m⁴)³ Write your answer using only positive exponents.

Answer 1

To simplify 2m⁶n⁴ / (6m⁴)³, we evaluate (6m⁴)³ to get 216m¹², then simplify the expression to get (1/108)m⁻⁶n⁴. Finally, we express m⁻⁶ with a positive exponent to obtain the final answer: n⁴ / (108m⁶).

Step-by-step explanation:

To simplify the given expression 2m⁶n⁴ / (6m⁴)³ with positive exponents, we need to evaluate the denominator and then simplify:

First, we compute the cube of 6m⁴ which is (6³)(m⁴³). This equals 216m¹² since 6 cubed is 216 and when we raise a power to a power, we multiply exponents.

Now our expression looks like this: 2m⁶n⁴ / 216m¹².

To simplify, we divide the coefficients (2/216) and subtract exponents of m, which results in: (1/108)m⁶−¹²n⁴. This further simplifies to (1/108)m⁻⁶n⁴ since 6 - 12 is -6.

Now, to have only positive exponents, we can rewrite m⁻⁶ as 1/m⁶. Thus, the simplified expression with only positive exponents is: (1/108)(1/m⁶)n⁴ or n⁴ / (108m⁶).