Question

Represent the following expressions as a power of the number a (a≠0): c ((a2)−2)5÷(a4a)3

Answer 1

Answer:

1/a²⁷

Step-by-step explanation:

Given: $\frac{((a^2)^{-2})^5}{a^4.a^3}$

We know that when the bases are same the powers can be added. i.,e.,

                                           (xᵃ)ᵇ = x ⁽ᵃ ⁺ ᵇ⁾

⇒ $\frac{((a^2)^{-2})^5}{a^4.a^3} \implies \frac{(a^2)^{-10}}{a^7}$

$ \implies \frac{a^{-20}}{a^7} = a^{-20 - 7} = a^{-27}$

Also, $\frac{x^a}{x^b} = x^{a - b}$

This is nothing but, $\frac{1}{a^{27}}$.

Note that $a$ cannot be zero here. The condition is provided in the question as well.