Solving Polynomials

Question

Simplify each expression. Final answer should be in standard form.

(-4m²n)⁴·1/6m^-10n^-4

I'm unsure on how to work this problem out step-by-step.

Answer 1

m^-10 and n^-4 can be moved to the numerator. Then combine like terms (such as the 4's and 6).

Then I get (-4*4/6)*(m^2)*(m^10)*(n)*(n^4) = (-8/3)*(m^12)*(n^5).

Answer 2

If that problem is what I am thinking, where the "2" represents a square number, then we have the following:

(-4m² n) (1/6)m^-10 n^-4

^{So, the first thing is to start by rewriting the middle term}

(1/6)m^-10 = 1/6m¹⁰

and the last term n^-4 = 1/n⁴

Now, let's rewrite what we have, including the first term:

-4m² n

6m¹⁰ n³

Then, the -4/6 simplifies to -2/3

Also, the m²/m¹⁰ simplifies to 1/m⁸

And, the n/n³ simplifies to 1/n²

Piecing all this together we get: -2/3 m^-8 n^-3

Or, if they want the answer with only positive exponents:

-2

3m⁸n³

So, the important part here is to remember that anything raised to a negative power is written as a fraction with 1 for the numerator all over "x" raised to whatever power they give you.

For example, x^-10 is equal to 1/x¹⁰ , note that the power of ten does not include the negative when written to its equivalent fraction form.

Any further questions, let me know. Thanks!