How do I solve this problem(properties of exponents?

Question

(-2m)^3h^7p^-5

/m^-1n^9p^-2

I'm trying to know how to solve this problems?

Answer 1

The short answer:

When you divide 2 similar expressions, the exponents subtract. If you multiply, the exponents add.

Examples:

x^4 / x^3 = x (exponent is 4 - 3 = 1

y^5 * y^7 = y^12

Watch out for like terms. For example: (2p)^4 * p^3. First, you have to factor out the constant term, so the problem looks like this: 2^4 * p^4 * p^3 which is then 16*p^7

Answer 2

(-2m)^3 * h^7 * p^-5

----------------------------

m^-1 * h^9 * p^-2

-8m^3 * h^7 * p^-5

----------------------------

m^-1 * h^9 * p^-2

when the bases are the same you subtract exponents; it's the top exponent minus the bottom exponent

-8m^(3-[-1])=-8m^4

h^(7-9)=h^-2

p^(-5-[-2])=p^-3

-8m^4 * h^-2 * p^-3

-8m^4 * (1/h^2) * (1/p^3)

-8m^4

---------

h^2p^3