Simplify this expression and put your answer in Scientific Notation: (5×10^6)×(2×10^−2)(4 points)

Question

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.

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Answer 1

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

Step 1: Simplify the coefficients

To combine the coefficients, multiply \( 5 \) and \( 2 \):

\[ 5 \times 2 = 10 \]

Step 2: Simplify the exponents

To combine the powers of ten, add the exponents:

\[ 10^6 \times 10^{-2} = 10^{6 + (-2)} = 10^{6 - 2} = 10^4 \]

Step 3: Change the exponent for Scientific Notation

Now we have:

\[ 10 \times 10^4 \]

This can be rewritten using the property of exponents \( a \times 10^n = (a \times 10^1) \times 10^{n-1} \):

\[ 10 \times 10^4 = 1.0 \times 10^5 \]

Step 4: Final answer

So, the final answer in Scientific Notation is:

\[ 1.0 \times 10^5 \]