Question

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

Answer 1

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