Simplification of Exponential Expression

MathematicsExponents and Scientific NotationEasySTEM

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$$9 \cdot 10^9 \frac{2 \cdot 10^{-6} \cdot 4 \cdot 10^{-4}}{6}$$

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1
Step 1

Let's solve this expression involving numbers written in scientific notation. We have nine times ten to the ninth, multiplied by two times ten to the negative sixth, and four times ten to the negative fourth, all divided by six.

Simplifying Scientific Notation

$$9 \cdot 10^9 \frac{2 \cdot 10^{-6} \cdot 4 \cdot 10^{-4}}{6}$$
2
Step 2

To make this easier, let's group all the numeric coefficients together and all the powers of ten together.

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Step 3

Now, let's simplify the coefficients. In the numerator, nine multiplied by two is eighteen, and eighteen times four is seventy-two.

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Step 4

Dividing seventy-two by six gives us twelve. So, the coefficient part of our answer is twelve.

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Step 5

Next, let's tackle the powers of ten. When multiplying powers with the same base, we simply add the exponents together.


$$x^a \cdot x^b = x^{a+b}$$

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About This Question

Subject
Mathematics
Topic
Exponents and Scientific Notation
Difficulty
Easy
Exam
STEM
Question Type
Open Ended

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