Simplify (3 square root of 243y^8)/( cube root of 9)

Math
3243y893
Simplify the numerator.
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Rewrite 243y8 as (9y4)2⋅3.
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Factor 81 out of 243.
381(3)y893
Rewrite 81 as 92.
392⋅3y893
Rewrite y8 as (y4)2.
392⋅3(y4)293
Move 3.
392(y4)2⋅393
Rewrite 92(y4)2 as (9y4)2.
3(9y4)2⋅393
3(9y4)2⋅393
Pull terms out from under the radical.
3⋅9y4393
Multiply 3 by 9.
27y4393
27y4393
Multiply 27y4393 by 932932.
27y4393⋅932932
Combine and simplify the denominator.
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Multiply 27y4393 and 932932.
27y4393293932
Raise 93 to the power of 1.
27y43932931932
Use the power rule aman=am+n to combine exponents.
27y43932931+2
Add 1 and 2.
27y43932933
Rewrite 933 as 9.
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Use axn=axn to rewrite 93 as 913.
27y43932(913)3
Apply the power rule and multiply exponents, (am)n=amn.
27y43932913⋅3
Combine 13 and 3.
27y43932933
Cancel the common factor of 3.
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Cancel the common factor.
27y43932933
Divide 1 by 1.
27y4393291
27y4393291
Evaluate the exponent.
27y439329
27y439329
27y439329
Cancel the common factor of 27 and 9.
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Factor 9 out of 27y43932.
9(3y43932)9
Cancel the common factors.
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Factor 9 out of 9.
9(3y43932)9(1)
Cancel the common factor.
9(3y43932)9⋅1
Rewrite the expression.
3y439321
Divide 3y43932 by 1.
3y43932
3y43932
3y43932
Rewrite 932 as (92)13.
3y43923
Raise 9 to the power of 2.
3y43813
Rewrite 81 as 33⋅3.
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Factor 27 out of 81.
3y4327(3)3
Rewrite 27 as 33.
3y4333⋅33
3y4333⋅33
Pull terms out from under the radical.
3y43(333)
Multiply 3y43(333).
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Multiply 3 by 3.
9y4333
Rewrite the expression using the least common index of 6.
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Use axn=axn to rewrite 33 as 313.
9y4(3133)
Rewrite 313 as 326.
9y4(3263)
Rewrite 326 as 326.
9y4(3263)
Use axn=axn to rewrite 3 as 312.
9y4(326⋅312)
Rewrite 312 as 336.
9y4(326⋅336)
Rewrite 336 as 336.
9y4(326336)
9y4(326336)
Combine using the product rule for radicals.
9y432⋅336
Multiply 32 by 33 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
9y432+36
Add 2 and 3.
9y4356
9y4356
9y4356
Raise 3 to the power of 5.
9y42436
Simplify (3 square root of 243y^8)/( cube root of 9)

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