Karen Morrison and Nick Hamshaw Solutions for Exercise 11: Examination practice

${\left(2x-2\right)}^{-3}$

Simplifying the above and writing the answer with positive indices only, we get $\frac{1}{8x^3-k{x}^2+kx-8}$.

Write the value of $k$.

If $x\ne 0$ and $y\ne 0$, simplify:

$3x^{\frac{1}{2}}\times 5x^{\frac{1}{2}}$

Simplifying ${\left(81y^6\right)}^{\frac{1}{2}}$ if $x\ne 0$ and $y\ne 0$, we get $9y^k$.

Write the value of $k$.

If $x\ne 0$ and $y\ne 0$, simplify:

${\left(64x^3\right)}^{\frac{1}{3}}$

${\left(\frac{1}{2}{x}^{\frac{2}{3}}\right)}^3$

Simplifying the above, we get $\frac{1}{k}{x}^2$.

Write the value of $k$.

${\left(3125t^{125}\right)}^{\frac{1}{5}}$

Simplifying the above, we get $k{t}^{25}$.

Write the value of $k$.

Find the value of $p$ when $3^p=\frac{1}{9}$

Find the value of $w$ when $x^{72}\times x^w=x^8$