Question

which shows the expression below in simplified form?
$(8 \times 10^4) \times (7 \times 10^{-2})$
\\(\bigcirc\\) a. \\(5.6 \times 10^2\\)
\\(\bigcirc\\) b. \\(5.6 \times 10^3\\)
\\(\bigcirc\\) c. \\(15 \times 10^2\\)

Explanation:

Step1: Multiply coefficients and powers

Multiply the coefficients \(8\) and \(7\), and use the rule \(a^m\times a^n = a^{m + n}\) for the powers of \(10\):
\((8\times7)\times(10^{4}\times10^{-2}) = 56\times10^{4 + (-2)}\)

Step2: Simplify the power and adjust coefficient

Simplify the exponent: \(10^{4-2}=10^{2}\). Now, rewrite \(56\times10^{2}\) in scientific notation (coefficient between \(1\) and \(10\)):
\(56\times10^{2}=5.6\times10^{1}\times10^{2}=5.6\times10^{3}\) (using \(a^m\times a^n = a^{m + n}\) again).

Answer:

B. \(5.6\times 10^{3}\)