could someone help me with math?

Question

Simplify this expression. If the answer contains exponents, all exponents should be positive.

(h⁵)^-3/h^-12

 

i'm so confused please help me!

Answer 1

(h⁵)^-3/h^-12

 

When raising a power to a power... multiply the exponents

 

(h⁵)^-3 = h^5(-3) = h^-15

 

So your problem is

 

h^-15/h^-12

 

Note that a^-n  = 1/aⁿ  and 1/a^-n = aⁿ

Move the h^-15 to the denominator and change sign on the exponent

 

h^-15/h^-12 = 1/(h¹⁵h^-12) = 1/h^15-12 = 1/h³

Answer 2

Hello Jared

You are given this expression (h⁵)^-3/h^-12   ---------------(1)

In eq(1) the outside (-3 is power of the inside (h⁵)

So the top stays the same because  bottom is in (3)

                           top of eq (1) = (h⁵)^-3  ----------------(2)

take the bottom from  eq (1)

                 1

1/h^-12  = -----   = h¹²                               ----------------(3)                      

             h^-12

Now  put the copies of the top and bottom in place of the left sides

                                            

(h⁵)^-3/ (h^-12)  =   (h⁵)^-3 (h)¹²              [multiply the inside (5) and outside(-3) power for (h⁵)^-3 ]

                    = (h)^-15 (h)¹²                 [Add -15 + 12 = -3]

                    = h^-3                            [ 1/h^-3 = h³ ; if '/' is removed you get positive power but lower]

                    = 1/h³