Question

By what number should ${(-3)}^7$ be divided so that the quotient may be equal to ${(-3)}^4$?

Answer 1

Let the the given number $(-3{)}^7$ divided by $x$ such that quotient will be ${(-3)}^4$.

$\Rightarrow \frac{(-3{)}^7}{x}=(-3{)}^4$

$\Rightarrow \frac{(-3{)}^7}{(-3{)}^4}=x$

$\Rightarrow (-3{)}^{7-4}=x$ [Using the identity $a^m÷a^n=a^{m-n}$]

$\Rightarrow (-3{)}^3=x$

$\therefore x=-27$ [$(-3{)}^3=-3\times -3\times -3=(-1{)}^3\times 27=-27$, as $(-1{)}^{\text{odd no.}}=-1$]

Therefore, the required number is $-27$