Answer
$\color{blue}{8 \times 10^5}$
Work Step by Step
RECALL:
The reciprocal of $a$ is $\dfrac{1}{a}$.
Thus, the reciprocal of $1.25 \times 10^{-6}$ is $\dfrac{1}{1.25 \times 10^{-6}}$.
Use the negative exponent rule ($a^{-m}=\dfrac{1}{a^m}, m\ne0$ to obtain:
$\dfrac{1}{1.25 \times 10^{-6}}
\\=\dfrac{1}{1.25 \times \frac{1}{10^6}}
\\=\dfrac{1}{1.25} \cdot \dfrac{10^6}{1}
\\=\dfrac{1 \times 10^6}{1.25}
\\=\dfrac{10^6}{1.25}$
Since $1.25 = \dfrac{5}{4}$, the expression above is equivalent to:
$=\dfrac{10^6}{\frac{5}{4}}
\\=10^6 \times \dfrac{4}{5}
\\=\dfrac{4}{5} \times 10^6$
With $\dfrac{4}{5}=0.8$, the expression above is equivalent to:
$=0.8 \times 10^6$
Since the constant (non-power of 10) part of a scientific notation must be greater than or equal to 1 but less than 10, write $0.8$ as $8 \times 10^{-1}$ to obtain:
$=8 \times 10^{-1} \times 10^6$
Using the rule $a^m \cdot a^n = a^{m+n}$, the expression above simplifies to:
$=8 \times 10^{-1+6}
\\=\color{blue}{8 \times 10^5}$
