# Combine square root of 2/100*(1)^2*(12/15)^2

2100⋅(1)2⋅(1215)2
Combine 2100 and (1)2.
2(1)2100⋅(1215)2
Reduce the expression 2(1)2100 by cancelling the common factors.
Factor 2 out of 2(1)2.
2((1)2)100⋅(1215)2
Factor 2 out of 100.
2(1)22⋅50⋅(1215)2
Cancel the common factor.
2(1)22⋅50⋅(1215)2
Rewrite the expression.
(1)250⋅(1215)2
(1)250⋅(1215)2
One to any power is one.
150⋅(1215)2
Rewrite 150 as 150.
150⋅(1215)2
Any root of 1 is 1.
150⋅(1215)2
Simplify the denominator.
Rewrite 50 as 52⋅2.
Factor 25 out of 50.
125(2)⋅(1215)2
Rewrite 25 as 52.
152⋅2⋅(1215)2
152⋅2⋅(1215)2
Pull terms out from under the radical.
152⋅(1215)2
152⋅(1215)2
Multiply 152 by 22.
152⋅22⋅(1215)2
Combine and simplify the denominator.
Multiply 152 and 22.
2522⋅(1215)2
Move 2.
25(22)⋅(1215)2
Raise 2 to the power of 1.
25(212)⋅(1215)2
Raise 2 to the power of 1.
25(2121)⋅(1215)2
Use the power rule aman=am+n to combine exponents.
2521+1⋅(1215)2
Add 1 and 1.
2522⋅(1215)2
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
25(212)2⋅(1215)2
Apply the power rule and multiply exponents, (am)n=amn.
25⋅212⋅2⋅(1215)2
Combine 12 and 2.
25⋅222⋅(1215)2
Cancel the common factor of 2.
Cancel the common factor.
25⋅222⋅(1215)2
Divide 1 by 1.
25⋅21⋅(1215)2
25⋅21⋅(1215)2
Evaluate the exponent.
25⋅2⋅(1215)2
25⋅2⋅(1215)2
25⋅2⋅(1215)2
Multiply 5 by 2.
210⋅(1215)2
Cancel the common factor of 12 and 15.
Factor 3 out of 12.
210⋅(3(4)15)2
Cancel the common factors.
Factor 3 out of 15.
210⋅(3⋅43⋅5)2
Cancel the common factor.
210⋅(3⋅43⋅5)2
Rewrite the expression.
210⋅(45)2
210⋅(45)2
210⋅(45)2
Simplify the expression.
Apply the product rule to 45.
210⋅4252
Raise 4 to the power of 2.
210⋅1652
Raise 5 to the power of 2.
210⋅1625
210⋅1625
Cancel the common factor of 2.
Factor 2 out of 10.
22(5)⋅1625
Factor 2 out of 16.
22⋅5⋅2⋅825
Cancel the common factor.
22⋅5⋅2⋅825
Rewrite the expression.
25⋅825
25⋅825
Multiply 25 and 825.
2⋅85⋅25
Simplify the expression.
Multiply 5 by 25.
2⋅8125
Move 8 to the left of 2.
82125
82125
The result can be shown in multiple forms.
Exact Form:
82125
Decimal Form:
0.09050966…
Combine square root of 2/100*(1)^2*(12/15)^2

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