Evaluate 64-1/2 x 1290002/32-4 x 30 x 52

• $64^{-1/2}$:

$$64^{-1/2} = \frac{1}{64^{1/2}} = \frac{1}{\sqrt{64}} = \frac{1}{8}$$

• $729000^{2/3}$:

$$729000^{2/3} = (729 \times 1000)^{2/3}$$ $$= (9^3 \times 10^3)^{2/3}$$ $$= ((9 \times 10)^3)^{2/3}$$ $$= (90^3)^{2/3}$$ $$= 90^2 = 8100$$

The numerator is $\frac{1}{8} \times 8100 = \frac{8100}{8} = \frac{2025}{2}$.

• $2^{-4}$:

$$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$$

• $3^0$:

$$3^0 = 1$$

• $5^2$:

$$5^2 = 25$$

The denominator is $\frac{1}{16} \times 1 \times 25 = \frac{25}{16}$.

$$\frac{\frac{2025}{2}}{\frac{25}{16}} = \frac{2025}{2} \times \frac{16}{25}$$ $$= \frac{2025 \times 16}{2 \times 25}$$

Simplify the fractions:

$$= \frac{2025}{25} \times \frac{16}{2}$$ $$= 81 \times 8$$ $$= 648$$

The evaluated expression is 648.