Can someone teach me how to solve the following problems in an easy to understand way? Appreciate any help!
Simplify and express with positive indices
6√a^4b x^6 *(a^2/3 x^-1 )
(16x^2/y^-2)^1/4
Simplify and express with positive indices
6√a^4b x^6 *(a^2/3 x^-1 )
(16x^2/y^-2)^1/4
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simplify √a^4 = √(a²)² = a²
6a²b x^6 *(a^2/3 )x^(-¹)
adding a² and a^²/³ =a(²+²/³) = a^(8/3)
adding
x^6 x^(-¹)= x^(6-1)=x^5
then put it back together
next
(16x^2/y^-2)^1/4
distribute the exponent (1/4)
(16)^1/4 (x²)^1/4 / (y-²)^1/4
= 2 x^( 2/4) /y^(-2/4) = 2 √x√y = 2√(xy)
6a²b x^6 *(a^2/3 )x^(-¹)
adding a² and a^²/³ =a(²+²/³) = a^(8/3)
adding
x^6 x^(-¹)= x^(6-1)=x^5
then put it back together
next
(16x^2/y^-2)^1/4
distribute the exponent (1/4)
(16)^1/4 (x²)^1/4 / (y-²)^1/4
= 2 x^( 2/4) /y^(-2/4) = 2 √x√y = 2√(xy)
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You are welcome my dear.
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[(16x^2)/(y^-2)]^(1/4)
= (16 x^2 y^2)^(1/4)
= (2^4 x^2 y^2)^(1/4)
= 2^(4/4) * (xy)^(2/4)
= 2 √xy
= (16 x^2 y^2)^(1/4)
= (2^4 x^2 y^2)^(1/4)
= 2^(4/4) * (xy)^(2/4)
= 2 √xy