# Simplify (-r^5s)^5(-r^4s^5)^4

(-r5s)5(-r4s5)4
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to -r5s.
(-r5)5s5(-r4s5)4
Apply the product rule to -r5.
(-1)5(r5)5s5(-r4s5)4
(-1)5(r5)5s5(-r4s5)4
Raise -1 to the power of 5.
-(r5)5s5(-r4s5)4
Multiply the exponents in (r5)5.
Apply the power rule and multiply exponents, (am)n=amn.
-r5⋅5s5(-r4s5)4
Multiply 5 by 5.
-r25s5(-r4s5)4
-r25s5(-r4s5)4
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to -r4s5.
-r25s5((-r4)4(s5)4)
Apply the product rule to -r4.
-r25s5((-1)4(r4)4(s5)4)
-r25s5((-1)4(r4)4(s5)4)
Multiply -1 by (-1)4 by adding the exponents.
Move (-1)4.
(-1)4⋅-1r25s5((r4)4(s5)4)
Multiply (-1)4 by -1.
Raise -1 to the power of 1.
(-1)4⋅(-1)1r25s5((r4)4(s5)4)
Use the power rule aman=am+n to combine exponents.
(-1)4+1r25s5((r4)4(s5)4)
(-1)4+1r25s5((r4)4(s5)4)
(-1)5r25s5((r4)4(s5)4)
(-1)5r25s5((r4)4(s5)4)
Raise -1 to the power of 5.
-r25s5((r4)4(s5)4)
Multiply the exponents in (r4)4.
Apply the power rule and multiply exponents, (am)n=amn.
-r25s5(r4⋅4(s5)4)
Multiply 4 by 4.
-r25s5(r16(s5)4)
-r25s5(r16(s5)4)
Multiply r25 by r16 by adding the exponents.
Move r16.
-(r16r25)s5(s5)4
Use the power rule aman=am+n to combine exponents.
-r16+25s5(s5)4
-r41s5(s5)4
-r41s5(s5)4
Multiply the exponents in (s5)4.
Apply the power rule and multiply exponents, (am)n=amn.
-r41s5s5⋅4
Multiply 5 by 4.
-r41s5s20
-r41s5s20
Multiply s5 by s20 by adding the exponents.
Move s20.
-r41(s20s5)
Use the power rule aman=am+n to combine exponents.
-r41s20+5