Exponentes y radicales

EXPONENTES Y RADICALES

Simplificar y expresar todas las respuestas en términos de exponentes positivos

(2^3 )(2^2 )=2^5
w^4 w^8=w^12
(x^3 x^5)/(y^9 y^5 )=x^8/y^14
(a^3 )^7/(b^4 )^5=a^21/b^20
(2x^2 y^3 )^3=2x^6 y^9
x^9/x^5 =x^4
(x^3 )^6/x(x^3 ) =x^18/x^4 =x^14

Evaluar las expresiones siguientes.
√25=5
√(7&-128)=-2
∜(1/16)=∜1/∜16=1/2
(49)^(1/2)=√49=79^(3/2)=√(2&9^3 )=√(2&729)=27
(32)^(-2/5)=1/〖32〗^(2/5) =1/√(5&〖32〗^2 )=1/√(5&1024)=1/4
(1/32)^(4/5)=1^(4/5)/〖32〗^(4/5) =√(5&1^4 )/√(5&〖34〗^4 )=√(5&1)/√(5&1,048,576)=1/16
Simplificar las expresionessiguientes:
√50=7.07
∛(2x^3 )=∛2x
√(16x^4 )=4x^2
2√8-5√27+∛128=15.3
(9z^4 )^(1/2)=(9)^(1/2)∙(z^4 )^(1/2)=3∙z^2=3z^2
((27t^3)/8)^(2/3)=((27)^(2/3) (t^3 )^(2/3))/∛64=(∛((〖27〗^2 ) ) t^2)/4=(∛((729) )t^2)/4=(9t^2)/4=9/4 t^2




Escribir las expresiones solamente en términos de exponentes positivos. Evitar los radicales en la forma final.
Ejemplo: y^(-1) √x=x^(1/2)/y
(a^5 b^(-3))/c^2=a^5/(c^2 b^3 )
5m^(-2) m^(-7)=5m^(-9)=5/m^9
(3t)^(-2)=1/(3t)^2 =1/(9t^2 )
√(5&5x^2 )=(5x)^(2/5)
√x-√y=(x)^(1/2) (y)^(1/2)
x^2 ∜(〖xy〗^(-2) z^3 )=x^2 (xy^(-2) z^3 )^(1/4)=x^2 (x^(1/4)y^((-2∙1/4) ) z^((3∙1/4) ) )=x^(9/4) y^(-1/2) z^(3/4)=(x^(9/4) z^(3/4))/y^(1/2)
Escribir las formas exponenciales usando radicales.
(2a-b+c)^(2/3)=∛((2a-b+c)^2 )
x^(4/5)=√(5&x^4 )3w^(-3/5)-(3w)^(-3/5)=(3w^(-3/5))/(-(3w)^(3/5) )=-3/(w^(3/5) (3w)^(3/5) )=-3/(√(5&w^3 )√(5&(3w)^3 ))=-3/(√(5&w^3 )√(5&〖9w〗^3 ))
Racionalizar los denominadores.
6/√5=6/5^(1/2) =6/5^(1/2) ∙5^(1/2)/5^(1/2) =(6√5)/54/√2x=4/(2x)^(1/2) =4/(2x)^(1/2) ∙(2x)^(1/2)/(2x)^(1/2) =(4√2x)/2x
1/∛3x=1/〖3x〗^(1/3) =1/〖3x〗^(1/3) ∙〖3x〗^(2/3)/〖3x〗^(2/3) =〖3x〗^(2/3)/3x=∛((3x)^2 )/3x
√12/√3=〖12〗^(1/2)/3^(1/2) =〖12〗^(1/2)/3^(1/2)∙〖12〗^(1/2)/3^(1/2) =12/3=4
√(5&2)/∜(a^2 b)=2^(1/5)/(a^2 b)^(1/4) =2^(1/5)/(a^2 b)^(1/4) ∙(a^2 b)^(3/4)/(a^2 b)^(3/4) =(√(5&2)∜((a^2 b)^3 ))/(a^2 b)=(√(5&2)∜(a^6 b^3 ))/(a^2 b)
Simplificar...