# Simplify ((2n^(1/3))(3n^(1/3)-4n^(4/3)))/(2n^(-1/3))

(2n13)(3n13-4n43)2n-13
Move n-13 to the numerator using the negative exponent rule 1b-n=bn.
(2n13)(3n13-4n43)n132
Multiply n13 by n13 by adding the exponents.
Move n13.
2(n13n13)(3n13-4n43)2
Use the power rule aman=am+n to combine exponents.
2n13+13(3n13-4n43)2
Combine the numerators over the common denominator.
2n1+13(3n13-4n43)2
2n23(3n13-4n43)2
2n23(3n13-4n43)2
Simplify terms.
Cancel the common factor.
2n23(3n13-4n43)2
Divide n23(3n13-4n43) by 1.
n23(3n13-4n43)
Apply the distributive property.
n23(3n13)+n23(-4n43)
Reorder.
Rewrite using the commutative property of multiplication.
3n23n13+n23(-4n43)
Rewrite using the commutative property of multiplication.
3n23n13-4n23n43
3n23n13-4n23n43
3n23n13-4n23n43
Simplify each term.
Multiply n23 by n13 by adding the exponents.
Move n13.
3(n13n23)-4n23n43
Use the power rule aman=am+n to combine exponents.
3n13+23-4n23n43
Combine the numerators over the common denominator.
3n1+23-4n23n43
3n33-4n23n43
Divide 3 by 3.
3n1-4n23n43
3n1-4n23n43
Simplify 3n1.
3n-4n23n43
Multiply n23 by n43 by adding the exponents.
Move n43.
3n-4(n43n23)
Use the power rule aman=am+n to combine exponents.
3n-4n43+23
Combine the numerators over the common denominator.
3n-4n4+23