Question

multiply. write your answer in scientific notation.
40·(5 × 10⁰)

Explanation:

Step1: Simplify \(10^0\)

Recall that any non - zero number to the power of 0 is 1, so \(10^0 = 1\). Then the expression \(5\times10^0\) becomes \(5\times1=5\).

Step2: Multiply 40 and 5

Now we have the expression \(40\times5\). Calculating this, we get \(40\times5 = 200\).

Step3: Convert to scientific notation

Scientific notation is of the form \(a\times10^n\) where \(1\leqslant a<10\) and \(n\) is an integer. We can write 200 as \(2\times10^2\) (since \(200=2\times100 = 2\times10^{2}\)). We can also do it by first re - expressing 40 in scientific notation. 40 can be written as \(4\times10^{1}\). Then the original expression \(40\times(5\times10^{0})\) can be rewritten as \((4\times10^{1})\times(5\times10^{0})\). Using the associative and commutative properties of multiplication for real numbers and exponents (\(a\times10^{m}\times b\times10^{n}=a\times b\times10^{m + n}\)), we have \((4\times5)\times(10^{1}\times10^{0})=20\times10^{1}\). But \(20 = 2\times10^{1}\), so \((2\times10^{1})\times10^{1}=2\times10^{1 + 1}=2\times10^{2}\).

Answer:

\(2\times10^{2}\)