Find the values of: 5. (g) 3ax2 x ax3 x a5 (d) 2x3 x (-3x2) (a) 35x9 (h) -2x3 x (-3x5y2) x (e) 3x-5 x (-4x-2) 6. Simplify. (a) 25 ÷ 23 (d) 82x5 ÷ 25x2 (e) -24x8 ÷ (-6x-2) 7. Simplify. (a) (23)2 (d) (-2x-2y4)5 (b) (X2)4 (e) (2x2)3 x (-3x2)3

Here are the solutions to the problems using the laws of indices.

3. Fill in the blank boxes with suitable numbers.

a)
The central value is $5^{20}$. We use the rule $a^m \times a^n = a^{m+n}$.

• Top box: $5^6 \times 5^2 \times 5^8 \times 5^{\boxed{4}} = 5^{6+2+8+4} = 5^{20}$
• Left box: $5^8 \times 5^{\boxed{12}} = 5^{8+12} = 5^{20}$
• Right box: $5^{15} \times