Question

divide.
\frac{7 \times 10^8}{1 \times 10^4}
options:
7 \times 10^8
6 \times 10^8
7 \times 10^4
6 \times 10^4

Explanation:

Step1: Separate coefficients and powers of 10

We can rewrite the fraction as the product of two fractions: one with the coefficients and one with the powers of 10. So, \(\frac{7\times10^{8}}{1\times10^{4}}=\frac{7}{1}\times\frac{10^{8}}{10^{4}}\)

Step2: Simplify the coefficient and the power of 10

The coefficient \(\frac{7}{1} = 7\). For the powers of 10, we use the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), so \(\frac{10^{8}}{10^{4}}=10^{8 - 4}=10^{4}\)

Step3: Multiply the results

Now we multiply the coefficient and the simplified power of 10: \(7\times10^{4}\)

Answer:

\(7\times 10^{4}\) (corresponding to the option "7 × 10⁴")