Question

Evaluate the expression (6*10^-5)*(5*10^-7)

Answer 1

To evaluate the expression \((6 \times 10^{-5}) \times (5 \times 10^{-7})\), you can use the property of multiplication for scientific notation, which states that you multiply the coefficients and add the exponents of the powers of ten.

1. Multiply the coefficients:
\[
6 \times 5 = 30
\]

2. Add the exponents of \(10\):
\[
-5 + (-7) = -12
\]

3. Combine the results:
\[
30 \times 10^{-12}
\]

Now, you can express this in proper scientific notation. Since \(30\) is not between \(1\) and \(10\), we convert it:
\[
30 = 3.0 \times 10^1
\]

So,
\[
30 \times 10^{-12} = (3.0 \times 10^{1}) \times 10^{-12} = 3.0 \times 10^{1 - 12} = 3.0 \times 10^{-11}
\]

Therefore, the value of the expression \((6 \times 10^{-5}) \times (5 \times 10^{-7})\) is:
\[
\boxed{3.0 \times 10^{-11}}
\]