1. **Problem statement:** Calculate the values of the following expressions: (iii) $\sqrt{3^2} \times 5^2$ (iv) $3^{-4}$ (b) Express $4 \times 2^{28}$ as $2^n$ and find $n$. 2. **Recall important rules:** - $\sqrt{a^2} = |a|$ (the positive root) - Negative exponents: $a^{-m} = \frac{1}{a^m}$ - Powers of powers: $a^m \times a^n = a^{m+n}$ 3. **Calculate (iii):** $$\sqrt{3^2} \times 5^2 = |3| \times 25 = 3 \times 25 = 75$$ 4. **Calculate (iv):** $$3^{-4} = \frac{1}{3^4} = \frac{1}{81}$$ 5. **Calculate (b):** Rewrite 4 as a power of 2: $$4 = 2^2$$ So, $$4 \times 2^{28} = 2^2 \times 2^{28} = 2^{2+28} = 2^{30}$$ Therefore, $$n = 30$$