Respuesta :
[tex] \sqrt{ \dfrac{25x^9y^3}{64x^6y^{11}} } = \\ \\
= \sqrt{ \dfrac{25x^3}{64y^{8}} } \\ \\
= \sqrt{ \dfrac{5\times 5x^2x}{8\times 8y^{4}y^4} } \\ \\
= \dfrac{5x}{8y^4}\sqrt{ x } \\ \\
= \dfrac{5x\sqrt{x}}{8y^4}
[/tex]
The equivalent expression of given expression is [tex]\bold{\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\frac{5}{8} \sqrt{\frac{x^{3}}{y^{8}} }}[/tex]
What are exponents?
It refers to the number of times a number is multiplied by itself."
How to multiply and divide fractional exponents?
"To multiply exponents with the same base, use the rule, [tex]x^a\times x^b=x^{a+b}[/tex] "
"To divide exponents with the same base, use the rule, [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]"
For given question,
We have been given an expression [tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }[/tex]
We need to find the equivalent expression of the given expression.
We use the rule of multiply and divide fractional exponents with the same base
[tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }\\\\= \sqrt{\frac{25times x^9\times y^3}{64times x^6\times y^{11}} }\\\\= \sqrt{\frac{25\times x^{9-6}\times y^3}{64\times y^{11}} }\\\\= \sqrt{\frac{25\times x^{3}\times y^{3-11}}{64}[/tex]
[tex]= \sqrt{\frac{25\times x^{3}\times y^{-8}}{64}[/tex]
[tex]= \sqrt{\frac{25\times x^{3}}{64\times y^{8}} }[/tex]
[tex]=\sqrt{\frac{25}{64}} \times \sqrt{\frac{x^{3}}{y^{8}} }[/tex]
[tex]=\frac{5}{8} \sqrt{\frac{x^{3}}{y^{8}} }[/tex]
Therefore, the equivalent expression of given expression is [tex]\bold{\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\frac{5}{8} \sqrt{\frac{x^{3}}{y^{8}} }}[/tex]
Learn more about exponents here:
https://brainly.com/question/5497425
#SPJ3
