Question

If a⁷ = 3, find the value of $\frac{(a^{-2})^{-3} \times (a^3)^4 \times (a^{-17})^{-1}}{a^7}$

Answer 1

Answer:

$\bf\frac{(a^{-2})^{-3}\times\:(a^3)^4\times\:(a^{-17})^{-1}}{a^7}=81$

Step-by-step explanation:

$\frac{(a^{-2})^{-3}\times\:(a^3)^4\times\:(a^{-17})^{-1}}{a^7}$

Using

$\boxed{(a^m)^n=a^{mn}}$

$=\frac{a^6\times\:a^{12}\times\:a^{17}}{a^7}$

Using

$\boxed{a^ma^n=a^{m+n}}$

$=\frac{a^{6+12+17}}{a^7}$

$=\frac{a^{35}}{a^7}$

Using

$\boxed{\frac{a^m}{a^n}=a^{m-n}}$

$=a^{35-7}$

$=a^{28}$

$=(a^7)^4$

$=(3)^4$

$=81$

$\implies\:\boxed{\frac{(a^{-2})^{-3}\times\:(a^3)^4\times\:(a^{-17})^{-1}}{a^7}=81}$