Question

evaluate the following expression using exponential rules. write the result in standard notation.
\\(\frac{0.3 \times 10^{-5}}{3 \times 10^{-7}}\\)
\\(\frac{0.3 \times 10^{-5}}{3 \times 10^{-7}} = \square\\)

Explanation:

Step1: Separate coefficients and exponents

We can split the fraction into the ratio of the coefficients and the ratio of the powers of 10. So, \(\frac{0.3\times10^{-5}}{3\times10^{-7}}=\frac{0.3}{3}\times\frac{10^{-5}}{10^{-7}}\)

Step2: Simplify the coefficient ratio

Calculate \(\frac{0.3}{3}\). Since \(0.3\div3 = 0.1\), we have \(\frac{0.3}{3}=0.1\)

Step3: Simplify the exponent ratio

Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\), for \(\frac{10^{-5}}{10^{-7}}\), we get \(10^{-5-(-7)}=10^{-5 + 7}=10^{2}\)

Step4: Multiply the results

Now, multiply the results from Step 2 and Step 3: \(0.1\times10^{2}\)

Step5: Convert to standard notation

\(0.1\times10^{2}=\frac{1}{10}\times100 = 10\)

Answer:

\(10\)