$${ 1 }^{ 2 } \times { 2 }^{ 2 } x { 4 }^{ 2 } \times { 5 }^{ 2 } =$$
$1600x$
$$1\times 2^{2}x\times 4^{2}\times 5^{2}$$
$$1\times 4x\times 4^{2}\times 5^{2}$$
$$4x\times 4^{2}\times 5^{2}$$
$$4x\times 16\times 5^{2}$$
$$64x\times 5^{2}$$
$$64x\times 25$$
$$1600x$$
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$1600$
$$\frac{\mathrm{d}}{\mathrm{d}x}(1\times 2^{2}x\times 4^{2}\times 5^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(1\times 4x\times 4^{2}\times 5^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x\times 4^{2}\times 5^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x\times 16\times 5^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(64x\times 5^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(64x\times 25)$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(1600x)$$
$$1600x^{1-1}$$
$$1600x^{0}$$
$$1600\times 1$$
$$1600$$
