Answer:
[tex](4f)^3 = 64*f^3[/tex]
[tex](-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4[/tex]
Step-by-step explanation:
Solving (a):
[tex](4f)^3[/tex]
Apply law of indices:
[tex]x^3 = x * x * x[/tex]
So, we have:
[tex](4f)^3 = 4f * 4f * 4f[/tex]
Rewrite as:
[tex](4f)^3 = 4 * 4 * 4*f*f*f[/tex]
[tex](4f)^3 = 64*f^3[/tex]
Solving (b):
[tex](-\frac{3}{2}t^2)^2[/tex]
Apply law of indices:
[tex]x * x = x^2[/tex]
So, we have:
[tex](-\frac{3}{2}t^2)^2 = (-\frac{3}{2}t^2) * (-\frac{3}{2}t^2)[/tex]
Remove brackets
[tex](-\frac{3}{2}t^2)^2 = -\frac{3}{2}t^2 * -\frac{3}{2}t^2[/tex]
Rewrite as:
[tex](-\frac{3}{2}t^2)^2 = -\frac{3}{2}*-\frac{3}{2}*t^2 * *t^2[/tex]
[tex](-\frac{3}{2}t^2)^2 = \frac{3}{2}*\frac{3}{2}*t^4[/tex]
[tex](-\frac{3}{2}t^2)^2 = \frac{9}{4}*t^4[/tex]
[tex](-\frac{3}{2}t^2)^2 = \frac{9}{4}t^4[/tex]
