# Simplify ((-2j^-3w^5)^-3)/((4j^-5w^-5)^2)

(-2j-3w5)-3(4j-5w-5)2
Move (-2j-3w5)-3 to the denominator using the negative exponent rule b-n=1bn.
1(4j-5w-5)2(-2j-3w5)3
Simplify the denominator.
Apply the product rule to 4j-5w-5.
1(4j-5)2(w-5)2(-2j-3w5)3
Apply the product rule to -2j-3w5.
1(4j-5)2(w-5)2(-2j-3)3(w5)3
Apply the product rule to 4j-5.
142(j-5)2(w-5)2(-2j-3)3(w5)3
Raise 4 to the power of 2.
116(j-5)2(w-5)2(-2j-3)3(w5)3
Multiply the exponents in (j-5)2.
Apply the power rule and multiply exponents, (am)n=amn.
116j-5⋅2(w-5)2(-2j-3)3(w5)3
Multiply -5 by 2.
116j-10(w-5)2(-2j-3)3(w5)3
116j-10(w-5)2(-2j-3)3(w5)3
Rewrite the expression using the negative exponent rule b-n=1bn.
1161j10(w-5)2(-2j-3)3(w5)3
Multiply the exponents in (w-5)2.
Apply the power rule and multiply exponents, (am)n=amn.
1161j10w-5⋅2(-2j-3)3(w5)3
Multiply -5 by 2.
1161j10w-10(-2j-3)3(w5)3
1161j10w-10(-2j-3)3(w5)3
Rewrite the expression using the negative exponent rule b-n=1bn.
1161j101w10(-2j-3)3(w5)3
Apply the product rule to -2j-3.
1161j101w10((-2)3(j-3)3)(w5)3
Raise -2 to the power of 3.
1161j101w10(-8(j-3)3)(w5)3
Multiply the exponents in (j-3)3.
Apply the power rule and multiply exponents, (am)n=amn.
1161j101w10(-8j-3⋅3)(w5)3
Multiply -3 by 3.
1161j101w10(-8j-9)(w5)3
1161j101w10(-8j-9)(w5)3
Rewrite the expression using the negative exponent rule b-n=1bn.
1161j101w10(-81j9)(w5)3
Multiply the exponents in (w5)3.
Apply the power rule and multiply exponents, (am)n=amn.
1161j101w10(-81j9)w5⋅3
Multiply 5 by 3.
1161j101w10(-81j9)w15
1161j101w10(-81j9)w15
1161j101w10(-81j9)w15
Simplify the denominator.
Combine 16 and 1j10.
116j10⋅1w10(-81j9)w15
Multiply 16j10 and 1w10.
116j10w10(-81j9)w15
Combine -8 and 16j10w10.
1-8⋅16j10w10⋅1j9w15
Multiply -8⋅16j10w10 and 1j9.
1-8⋅16j10w10j9w15
Combine -8⋅16j10w10j9 and w15.
1-8⋅16w15j10w10j9
1-8⋅16w15j10w10j9
Multiply -8 by 16.
1-128w15j10w10j9
Multiply j10 by j9 by adding the exponents.
Move j9.
1-128w15j9j10w10
Use the power rule aman=am+n to combine exponents.
1-128w15j9+10w10
Add 9 and 10.
1-128w15j19w10
1-128w15j19w10
Simplify the denominator.
Reduce the expression -128w15j19w10 by cancelling the common factors.
Factor w10 out of -128w15.
1w10(-128w5)j19w10
Factor w10 out of j19w10.
1w10(-128w5)w10j19
Cancel the common factor.
1w10(-128w5)w10j19
Rewrite the expression.
1-128w5j19
1-128w5j19
Move the negative in front of the fraction.
1-128w5j19
1-128w5j19
Cancel the common factor of 1 and -1.
Rewrite 1 as -1(-1).
-1(-1)-128w5j19
Move the negative in front of the fraction.
-1128w5j19
-1128w5j19
Multiply the numerator by the reciprocal of the denominator.
-(1j19128w5)
Multiply j19128w5 by 1.
-j19128w5
Simplify ((-2j^-3w^5)^-3)/((4j^-5w^-5)^2)

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