Karen Morrison and Nick Hamshaw Solutions for Exercise 9: Exercise 2.9

Simplify. Write your answer using only positive indices.

$x^{-3}\times x^4$

On simplifying and writing our answer using only positive indices of $2x^{-3}\times 3x^{-3}$ we get $\frac{k}{x^6}$. Find the value of $k$.

If $4x^3÷12x^7=\frac{1}{k{x}^m}$, then find the value of $\left(k+m\right)$.

If $\frac{x^{-7}}{x^4}=x^k$, the find the value of $k$.

If ${\left(2x^2\right)}^{-3}=\frac{1}{k{x}^m}$, then find the value of $\left(k+m\right)$.

If ${\left(x^{-2}\right)}^3=\frac{1}{x^k}$, then find the value of $k$.

If $\frac{x^{-3}}{x^{-4}}=x^k$, then find the value of $k$.

If $\frac{x^{-2}}{x^3}=x^k$, then find the value of $k$.