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(x^5*y^6)^1/5(x^3*y^4)^1/4=x^m/4*y^n/5
If the equation above, where m and n are constants, is true for all positive values of x and y, what is the value of m+n?

Respuesta :

ajeigbeibraheem

If m and n are constants and it is true for all positive values of x and y, the value of m+n is 7+11 = 18

What is the simplification of the given algebra?

The simplification of the given algebra can be evaluated by using the law of indices.

Given that:

[tex]\mathbf{=(x^5y^6)^{1/5}(x^3y^4)^{1/4}}[/tex]

[tex]\mathbf{=xy^{6/5}(x^3y^4)^{1/4} }[/tex]

Simplifying using the multiplication power rule.

[tex]\mathbf{=xy^{6/5}(x^{3/4}y)}[/tex]

[tex]\mathbf{=xy^{6/5} \times (x^{3/4}y)}[/tex]

Multiplying like terms.

[tex]\mathbf{=x^{\frac{4+3}{4}} y^{\frac{6+5}{5}}}[/tex]

[tex]\mathbf{=x^{\frac{7}{4}} y^{\frac{11}{5}}}[/tex]

where;

  • m = 7 and n = 11

The value of m+n = 7+11 = 18.

Learn more about simplifying algebra expressions here:

https://brainly.com/question/2164351

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