Question

evaluate the expression
$(7 \times 10^5) \div (7 \times 10^{-8})$
$10^{13}$ $10^{-13}$ $10^3$ $10^{-3}$

Explanation:

Step1: Separate coefficients and powers

We can rewrite the division as the division of the coefficients and the division of the powers of 10 separately. So, \((7\times10^{5})\div(7\times10^{-8})=\frac{7}{7}\times\frac{10^{5}}{10^{-8}}\)

Step2: Simplify the coefficient

The coefficient part \(\frac{7}{7} = 1\)

Step3: Simplify the power of 10

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), for \(\frac{10^{5}}{10^{-8}}\), we have \(10^{5-(-8)}=10^{5 + 8}=10^{13}\)

Step4: Multiply the results

Since the coefficient is 1, multiplying by \(10^{13}\) gives \(1\times10^{13}=10^{13}\)

Answer:

\(10^{13}\)