Answer:
[tex]\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}[/tex]
Step-by-step explanation:
Let us revise the properties of exponents
Let us use these properties to solve the question
→ By using the 3rd property above
∵ [tex](a^{2})^{3}=a^{2.3}=a^{6}[/tex]
∴ [tex]\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10} }[/tex]
→ By using the 1st property above
∵ [tex]a^{6}.a^{-3}=a^{6+-3}=a^{6-3}=a^{3}[/tex]
∴ [tex]\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}[/tex]
→ By using the 2nd property above
∵ [tex]\frac{a^{3}}{a^{10}}=a^{3-10}=a^{-7}[/tex]
∴ [tex]\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}[/tex]
→ By using the 4th property above
∵ [tex]a^{-7}=\frac{1}{a^{7}}[/tex]
∴ [tex]\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}[/tex]
