# Simplify ((4p)^2p^3)/(p^-1p^-5)*(4p^-4)^-3

(4p)2p3p-1p-5⋅(4p-4)-3
Simplify the numerator.
Apply the product rule to 4p.
42p2p3p-1p-5⋅(4p-4)-3
Multiply p2 by p3 by adding the exponents.
Move p3.
42(p3p2)p-1p-5⋅(4p-4)-3
Use the power rule aman=am+n to combine exponents.
42p3+2p-1p-5⋅(4p-4)-3
42p5p-1p-5⋅(4p-4)-3
42p5p-1p-5⋅(4p-4)-3
Raise 4 to the power of 2.
16p5p-1p-5⋅(4p-4)-3
16p5p-1p-5⋅(4p-4)-3
Multiply p-1 by p-5 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
16p5p-1-5⋅(4p-4)-3
Subtract 5 from -1.
16p5p-6⋅(4p-4)-3
16p5p-6⋅(4p-4)-3
Rewrite the expression using the negative exponent rule b-n=1bn.
16p51p6⋅(4p-4)-3
Multiply the numerator by the reciprocal of the denominator.
16p5p6⋅(4p-4)-3
Multiply p5 by p6 by adding the exponents.
Move p6.
16(p6p5)⋅(4p-4)-3
Use the power rule aman=am+n to combine exponents.
16p6+5⋅(4p-4)-3
16p11⋅(4p-4)-3
16p11⋅(4p-4)-3
Rewrite the expression using the negative exponent rule b-n=1bn.
16p11⋅(41p4)-3
Combine 4 and 1p4.
16p11⋅(4p4)-3
Change the sign of the exponent by rewriting the base as its reciprocal.
16p11⋅(p44)3
Simplify the expression.
Apply the product rule to p44.
16p11⋅(p4)343
Multiply the exponents in (p4)3.
Apply the power rule and multiply exponents, (am)n=amn.
16p11⋅p4⋅343
Multiply 4 by 3.
16p11⋅p1243
16p11⋅p1243
Raise 4 to the power of 3.
16p11⋅p1264
16p11⋅p1264
Cancel the common factor of 16.
Factor 16 out of 16p11.
16(p11)⋅p1264
Factor 16 out of 64.
16(p11)⋅p1216(4)
Cancel the common factor.
16p11⋅p1216⋅4
Rewrite the expression.
p11⋅p124
p11⋅p124
Combine p11 and p124.
p11p124
Multiply p11 by p12 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
p11+124