Respuesta :
Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].
What are equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].
[tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
[tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]
[tex]$\sqrt{8}=2 \sqrt{2}$[/tex]
[tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]
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The complete question is :
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
