In Exercises 51–58, solve each equation. Express the solution in ...

Question

In Exercises 51–58, solve each equation. Express the solution in scientific notation.

x / 2X10⁸ =-3.1X10⁻⁵

Accepted Answer

Welcome back. I am so glad you're here. We are given this practice problem we're told for the following equation. Work out the value of X, right. The final answer and scientific notation, the equation that we're given is X divided by five times 10, raised to the ninth and that is equal to negative 6.5 times 10, raised to the negative sixth. Our answer choices are a negative 1. times 10 to the third. B negative 1.3 times 10 to the fourth, C negative 3.25 times 10 to the third and D negative 3.25 times 10 to the fourth. Alright, I want to point out the X that we are solving for is this one here in the numerator. On the left hand side, the other X's denote multiplication. And now in order to get that X by itself, it is being divided by five times 10 to the ninth. We can multiply both sides of the equation by five times 10 to the ninth. What we do to one side we do to the other as well. So on the left, those five times 10 to the ninth cancel out and we just have X which is what we want. And on the right, we have a negative 6.5 times 10 to the negative six times five times to the ninth. And what we can do here is multiply the parts that are alike so we can take the negative 6.5 times five. And when we multiply those, we get negative 32.5 and then the other parts that are alike are these tens, they are similar bases and they have different exponents. So when we have the same base and that's being multiplied, what we do is we add the exponents. So we take negative six plus nine and negative six plus nine equals a positive three. So have negative 32.5 times 10, that base raised to the now positive three. Well, this is very close. We almost have this in scientific notation. However, we recall from previous lessons that for scientific notation, we have one unit between one and nine in front of the decimal point. And right now we have two units, we have that three in the two for 32. So we need to move the decimal one unit to the left. And whenever we move a decimal and we move it to the left, we are going to raise the exponents of this 10 to the. So the three will be at, it will have added to it however many places we move the decimal point, we moved at one place. So we're adding one to the three, three plus one equals four. So we have negative 3.25 times 10 raised to the fourth. And that is our answer and scientific notation, we look at our answer choices for negative 3.25 times 10 to the fourth. And that matches with answer choice D well done. We'll catch you on the next one.

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In Exercises 51–58, solve each equation. Express the solution in scientific notation. x / 2X10⁸ =-3.1X10⁻⁵