Simplify this expression and put your answer in Scientific Notation: (5×10^(6))×(2×10^(−2))

Question

(4 points)
Step 1:
the coefficients

Step 2:
the exponents to simplify.

Step 3:
to change the exponent for Scientific Notation

Step 4:
is the final answer.

Answer 1

Let's simplify the expression \((5 \times 10^{6}) \times (2 \times 10^{-2})\) step by step:

Step 1: Multiply the coefficients

Multiply the coefficients 5 and 2: \[ 5 \times 2 = 10 \]

Step 2: Add the exponents

When multiplying powers of 10, we add the exponents: \[ 10^{6} \times 10^{-2} = 10^{6 + (-2)} = 10^{4} \]

Step 3: Put into Scientific Notation

Now combine the results from Step 1 and Step 2: \[ 10 \times 10^{4} \] This can be rewritten as: \[ 10^{1} \times 10^{4} = 10^{1 + 4} = 10^{5} \]

Step 4: Final answer

So the final answer in Scientific Notation is: \[ 1.0 \times 10^{5} \]

Thus, the full simplified expression in scientific notation is: \[ \boxed{1.0 \times 10^{5}} \]