# Solve for r 3=81*r^(10-1) 3=81⋅r10-1
Rewrite the equation as 81⋅r10-1=3.
81⋅r10-1=3
Subtract 1 from 10.
81⋅r9=3
Divide each term by 81 and simplify.
Divide each term in 81⋅r9=3 by 81.
81⋅r981=381
Cancel the common factor of 81.
Cancel the common factor.
81⋅r981=381
Divide r9 by 1.
r9=381
r9=381
Cancel the common factor of 3 and 81.
Factor 3 out of 3.
r9=3(1)81
Cancel the common factors.
Factor 3 out of 81.
r9=3⋅13⋅27
Cancel the common factor.
r9=3⋅13⋅27
Rewrite the expression.
r9=127
r9=127
r9=127
r9=127
Take the 9th root of both sides of the equation to eliminate the exponent on the left side.
r=1279
Simplify 1279.
Rewrite 1 as 13.
r=13279
Rewrite 27 as 33.
r=13339
Rewrite 1333 as (13)3.
r=(13)39
Rewrite (13)39 as (13)333.
r=(13)333
Pull terms out from under the radical, assuming real numbers.
r=133
Rewrite 133 as 1333.
r=1333
Any root of 1 is 1.
r=133
Multiply 133 by 332332.
r=133⋅332332
Combine and simplify the denominator.
Multiply 133 and 332332.
r=33233332
Raise 33 to the power of 1.
r=332331332
Use the power rule aman=am+n to combine exponents.
r=332331+2
Add 1 and 2.
r=332333
Rewrite 333 as 3.
Use axn=axn to rewrite 33 as 313.
r=332(313)3
Apply the power rule and multiply exponents, (am)n=amn.
r=332313⋅3
Combine 13 and 3.
r=332333
Cancel the common factor of 3.
Cancel the common factor.
r=332333
Divide 1 by 1.
r=33231
r=33231
Evaluate the exponent.
r=3323
r=3323
r=3323
Simplify the numerator.
Rewrite 332 as (32)13.
r=3233
Raise 3 to the power of 2.
r=933
r=933
r=933
The result can be shown in multiple forms.
Exact Form:
r=933
Decimal Form:
r=0.69336127…
Solve for r 3=81*r^(10-1)

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