Respuesta :
Answer:
The expression is equivalent to[tex]A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}[/tex] is [tex]\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}[/tex].
Step-by-step explanation:
The expression provided is:
[tex]A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}[/tex]
Simplify the expression A as follows:
[tex]A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}[/tex]
[tex]=\sqrt[4]{\frac{24}{128}\times x^{(6-4)}\times y^{(1-5)}}\\\\=\sqrt[4]{\frac{3}{16}\times x^{2}\times y^{-4}}\\\\=[\frac{3}{16}\times x^{2}\times y^{-4}]^{1/4}\\\\=[\frac{3}{16}]^{1/4}\times x^{(2\times (1/4))}\times y^{(-4\times (1/4))}\\\\=\frac{\sqrt[4]{3}}{2}}\times x^{1/2}\times y^{-1}\\\\=\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}[/tex]
Thus, the expression is equivalent to[tex]A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}[/tex] is [tex]\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}[/tex].
Equivalent expressions are expressions that have equal values
The equivalent expression of [tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}[/tex] is [tex]\frac 1{2y}\sqrt[4]{ 3x^2}}[/tex]
The expression is given as:
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}[/tex]
Divide 24 and 128 by 8
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \sqrt[4]{ \frac{3x^6y}{16x^4y^5}}[/tex]
Take 4th root of 16
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ \frac{3x^6y}{x^4y^5}}[/tex]
Apply law of indices, to simplify the fraction
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ 3x^{6-4}y^{1-5}}[/tex]
Simplify
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ 3x^{2}y^{-4}}[/tex]
Rewrite as:
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 12\sqrt[4]{ \frac{3x^{2}}{y^4}}[/tex]
Take 4th root of y^4
[tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}= \frac 1{2y}\sqrt[4]{ 3x^2}}[/tex]
Hence, the equivalent expression of [tex]\sqrt[4]{ \frac{24x^6y}{128x^4y^5}}[/tex] is [tex]\frac 1{2y}\sqrt[4]{ 3x^2}}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/15715866
