Simplify 4/( cube root of 9y^4)

Math
49y43
Simplify the denominator.
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Rewrite 9y4 as y3⋅(9y).
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Factor out y3.
49(y3y)3
Reorder 9 and y3.
4y3⋅9y3
Add parentheses.
4y3⋅(9y)3
4y3⋅(9y)3
Pull terms out from under the radical.
4y9y3
4y9y3
Multiply 4y9y3 by 9y329y32.
4y9y3⋅9y329y32
Combine and simplify the denominator.
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Multiply 4y9y3 and 9y329y32.
49y32y9y39y32
Move 9y3.
49y32y(9y39y32)
Raise 9y3 to the power of 1.
49y32y(9y319y32)
Use the power rule aman=am+n to combine exponents.
49y32y9y31+2
Add 1 and 2.
49y32y9y33
Rewrite 9y33 as 9y.
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Use axn=axn to rewrite 9y3 as (9y)13.
49y32y((9y)13)3
Apply the power rule and multiply exponents, (am)n=amn.
49y32y(9y)13⋅3
Combine 13 and 3.
49y32y(9y)33
Cancel the common factor of 3.
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Cancel the common factor.
49y32y(9y)33
Divide 1 by 1.
49y32y(9y)1
49y32y(9y)1
Simplify.
49y32y(9y)
49y32y(9y)
49y32y(9y)
Multiply y by y by adding the exponents.
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Move y.
49y32y⋅y⋅9
Multiply y by y.
49y32y2⋅9
49y32y2⋅9
Simplify the numerator.
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Rewrite 9y32 as ((9y)2)13.
4(9y)23y2⋅9
Apply the product rule to 9y.
492y23y2⋅9
Raise 9 to the power of 2.
481y23y2⋅9
Rewrite 81y2 as 33⋅(3y2).
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Factor 27 out of 81.
427(3)y23y2⋅9
Rewrite 27 as 33.
433⋅3y23y2⋅9
Add parentheses.
433⋅(3y2)3y2⋅9
433⋅(3y2)3y2⋅9
Pull terms out from under the radical.
4⋅33y23y2⋅9
Multiply 4 by 3.
123y23y2⋅9
123y23y2⋅9
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 12 and 9.
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Factor 3 out of 123y23.
3(43y23)y2⋅9
Cancel the common factors.
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Factor 3 out of y2⋅9.
3(43y23)3(y2⋅3)
Cancel the common factor.
3(43y23)3(y2⋅3)
Rewrite the expression.
43y23y2⋅3
43y23y2⋅3
43y23y2⋅3
Move 3 to the left of y2.
43y233y2
43y233y2
Simplify 4/( cube root of 9y^4)

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