Simplify (1.25 x 10⁴) + (2.0 x 10⁴) / (6.25 x 10⁵)

Since both terms in the numerator have the same power of 10 ($10^4$), we can add their coefficients directly.

$$(1.25 \times 10^4) + (2.0 \times 10^4) = (1.25 + 2.0) \times 10^4 = 3.25 \times 10^4$$

Now we have:

$$\frac{3.25 \times 10^4}{6.25 \times 10^5}$$

We can separate the coefficients and the powers of 10:

$$\left(\frac{3.25}{6.25}\right) \times \left(\frac{10^4}{10^5}\right)$$

$$\frac{3.25}{6.25} = \frac{325}{625}$$

Dividing both numerator and denominator by 25:

$$\frac{325 \div 25}{625 \div 25} = \frac{13}{25} = 0.52$$

Using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$:

$$\frac{10^4}{10^5} = 10^{4-5} = 10^{-1}$$

$$0.52 \times 10^{-1}$$

To express this in standard scientific notation (where the coefficient is between 1 and 10), we move the decimal point one place to the right and adjust the exponent:

$$0.52 \times 10^{-1} = 5.2 \times 10^{-2}$$

The simplified expression is:

$$5.2 \times 10^{-2}$$