y to the -8 power times y to the 2nd power. simplify

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doc.brown · Answer

$$y^{-8}=\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}$$$$y^2=y\times y$$$$y^{-8}\times {y^2}=\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times y\times y$$$$=\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{y}{y}\times\frac{y}{y}$$$$=\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times1\times1$$$$\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}\times\frac{1}{y}=y^{-6}$$$$y^{-8}\times y^{2}=y^{-6}$$See how -8+2=-6?
or the rule:$$x^a\times x^b=x^{a+b}$$