Question

h) $\frac{(4^{3})^{3}(5^{-2})}{(5^{2})^{-2}(4^{2})^{4}}$

Explanation:

Step1: Apply exponent power rule

$(a^m)^n = a^{m \times n}$
$\frac{(4^{3 \times 3})(5^{2 \times 1})}{(5^{2 \times -2})(4^{2 \times 4})} = \frac{4^9 \times 5^2}{5^{-4} \times 4^8}$

Step2: Rearrange like bases

Group terms with same base together
$\frac{4^9}{4^8} \times \frac{5^2}{5^{-4}}$

Step3: Apply quotient exponent rule

$\frac{a^m}{a^n} = a^{m-n}$
$4^{9-8} \times 5^{2 - (-4)} = 4^1 \times 5^{6}$

Step4: Calculate final values

Compute the numerical results
$4 \times 15625$

Answer:

$62500$