Equivalent expressions are expressions that have the same value
The equivalent expression of [tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}}[/tex] is [tex]-2x^{8}y^{18}[/tex]
The expression is given as:
[tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}}[/tex]
Divide the common terms in the above expression
[tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}} = -\frac{2x^6y^{12}}{x^{-2}y^{-6}}[/tex]
Combine expression with the same base, by applying the law of indices
[tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}} = -2x^{6--2}y^{12--6}[/tex]
Rewrite the exponents as follows
[tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}} = -2x^{6+2}y^{12+6}[/tex]
Evaluate the exponents
[tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}} = -2x^{8}y^{18}[/tex]
Hence, the equivalent expression of [tex]\frac{10x^6y^{12}}{-5x^{-2}y^{-6}}[/tex] is [tex]-2x^{8}y^{18}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
