3. Solve for the unknown variable x. [2 marks each] a) x^5=-1024 b) x^(3)/(5)=27

## Step 1: Isolate x in equation a)<br />### To solve for $x$, we need to take the fifth root of both sides of the equation $x^5 = -1024$. This will isolate $x$ and give us its value.<br />## Step 2: Calculate the fifth root<br />### The fifth root of -1024 is -4, since $(-4)^5 = -1024$.<br />## Step 3: Isolate x in equation b)<br />### To isolate $x$ in the equation $x^{\frac{3}{5}} = 27$, we raise both sides of the equation to the power of $\frac{5}{3}$, the reciprocal of $\frac{3}{5}$. This gives us $(x^{\frac{3}{5}})^{\frac{5}{3}} = 27^{\frac{5}{3}}$.<br />## Step 4: Simplify and calculate<br />### Simplifying the left side gives us $x$. The right side can be rewritten as $(27^{\frac{1}{3}})^5$, which is $3^5 = 243$.