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How do you simplify #64(x^{4}y^{3})^{\frac{5}{6}}#?

Answer 1

Gianna Caruso

#64(x^4y^3)^(5/6)=64x^3y^2root(3)xsqrty#

Remember #(ab)^m=a^mb^m# and #(a^m)^n=a^(mn)#

Hence #64(x^4y^3)^(5/6)#

= #64xx(x^4)^(5/6)xx(y^3)^(5/6)#

= #64xx x^(4xx5/6)xxy^(3xx5/6)#

= #64xx x^(20/6)xxy^(15/6)#

= #64xx x^((color(red)2xx10)/(color(red)2xx3))xxy^((color(red)3xx5)/(color(red)3xx2))#

= #64xx x^(10/3)xxy^(5/2)#

= #64xx x^(3+1/3)xxy^(2+1/2)#

= #64xx x^3x^(1/3)y^2y^(1/2)#

= #64x^3y^2root(3)xsqrty#

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Answer 2

Everly Taylor

To simplify ( 64(x^{4}y^{3})^{\frac{5}{6}} ), you can follow these steps:

Recognize that ( 64 = 2^6 ).
Apply the exponent property ( (a^m)^n = a^{m \cdot n} ).
Simplify the expression inside the parentheses.
Combine the exponents.

The simplified expression is ( 32x^{\frac{10}{3}}y^{\frac{5}{2}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.