Answer: -16x11y18
—————————
3
Step-by-step explanation:
2
Simplify —
3
Equation at the end of step 1 :
2
((0-(3x•(y2)))3)•((0-((—•x2)•(y3)))4)
3
Step 2 :
Equation at the end of step 2 :
2x2
((0-(3x•(y2)))3)•((0-(———•(y3)))4)
3
Step 3 :
Equation at the end of step 3 :
(2x2y3)
((0-(3x•(y2)))3)•((0-———————)4)
3
Step 4 :
4.1 Negative number raised to an even power is positive
For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :
(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)
Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive.
We proved that (-7)6 is equal to (7)6 which is a positive number
Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved
4.2 x2 raised to the 4 th power = x( 2 * 4 ) = x8
4.3 y3 raised to the 4 th power = y( 3 * 4 ) = y12
Equation at the end of step 4 :
24x8y12
((0 - (3x • (y2)))3) • ———————
34
Step 5 :
Equation at the end of step 5 :
24x8y12
((0 - (3xy2))3) • ———————
34
Step 6 :
Multiplying exponential expressions :
6.1 x3 multiplied by x8 = x(3 + 8) = x11
Multiplying exponential expressions :
6.2 y6 multiplied by y12 = y(6 + 12) = y18
Dividing exponents :
6.3 33 divided by 34 = 3(3 - 4) = 3(-1) = 1/31 = 1/3
