Equivalent expressions are expressions that have equal values
The equivalent expressions of [tex]y^{-8}y^3x^0x^{-2}[/tex] are [tex]x^{-2}y^{-5}[/tex] and [tex]\frac{1}{x^2y^5}[/tex]
The expression is given as:
[tex]y^{-8}y^3x^0x^{-2}[/tex]
Express x^0 as 1
[tex]y^{-8}y^3x^0x^{-2} = y^{-8}y^3 \times 1 \times x^{-2}[/tex]
Apply law of indices
[tex]y^{-8}y^3x^0x^{-2} = y^{-8 + 3}\times x^{-2}[/tex]
[tex]y^{-8}y^3x^0x^{-2} = y^{-5}\times x^{-2}[/tex]
Remove the product sign (x)
[tex]y^{-8}y^3x^0x^{-2} = y^{-5}x^{-2}[/tex]
Rewrite as:
[tex]y^{-8}y^3x^0x^{-2} = x^{-2}y^{-5}[/tex]
Rewrite as positive exponents
[tex]y^{-8}y^3x^0x^{-2} = \frac{1}{x^2y^5}[/tex]
Hence, the equivalent expressions of [tex]y^{-8}y^3x^0x^{-2}[/tex] are [tex]x^{-2}y^{-5}[/tex] and [tex]\frac{1}{x^2y^5}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
