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.(-1.2X10⁻³)x=(1.8X10⁻⁴)(2.4X10⁶)

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 in scientific notation, the equation we're given is parentheses, five times 10, raised to the negative fourth and parentheses times X equals parentheses three, 3.5 times 10, raised to the negative fifth and parentheses and then times new parentheses, 1.2 times 10 raised to the eighth power and parentheses. The X we're looking for is right here in front of the equal sign on the left hand side. Those other exes are for multiplication. Our answer choices are a 8.4 times 10 to the sixth, be 8.4 times 10 to the seventh C 2.1 times 10 to the zero and D 2. times 10 to the first. All right. Now to solve for X. On the left hand side, we want to get that X by itself. And in order to do that, we're going to divide it by the factor it's being multiplied by. So we're going to divide it by parentheses five times raised to the negative fourth and what we do to one side, we need to do to the other side. So we're dividing both sides by five times 10, raised to the negative fourth. And now that gets us X by itself on the left hand side. Great. Now it's just a matter of simplifying what's on the right hand side. So we have 3.5 times 10 to the negative fifth times 1.2 times 10 to the eighth. In the numerator, we need to combine those two. And in order to do that, we are going to multiply the parts that are like, so we'll be multiplying the 3.5 times the 1.2 And 3.5 times 1.2 equals 4.2. And now we are going to multiply the 10 to the negative fifth times the 10 to the eighth. Well, the bases remain the same. So this is 4.2 times 10. And when we have a base with exponents being multiplied, we are going to add those exponents. So we're taking negative five plus eight and negative five plus eight is a positive three. Alright, we've simplified that numerator that's all over five times 10 to the negative fourth. Now, very similarly, we're going to do the division for the parts that are alike. So we're going to take the 4.2 divided by five, 4.2, divided by five equals 0. and then we have the times 10 to the third in the numerator and the times 10 to the negative fourth in the denominator. Again, we've got two bases, the same base with exponents. Now they're being divided and we recall from previous lessons that when we have bases that have exponents and they're being divided, we are going to subtract the exponents. So this time, we're going to take three minus negative four and three minus negative four is three plus four. So that is seven. So we've got 0.84 times 10 raised to the new exponents is seventh. Well, this is close to being simplified. However, it says to write the final answer in scientific notation and we recall from previous lessons that there has to be one number in front of the decimal point that is between one and nine for scientific notation. So what we need to do to get that to happen is we need to move this decimal place one to the right. So it's going to be 8. times 10 to the. But now whenever we move a decimal point to the right, we are going to lower our exponent for the to the and we're going because we moved it to the right one space, we're going to move it down one, we're going to subtract one. So seven minus one that equal six. So we've got 8.4 times 10 to the sixth power looking at our answer choices that matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 51–58, solve each equation. Express the solution in scientific notation.(-1.2X10⁻³)x=(1.8X10⁻⁴)(2.4X10⁶)

Key Concepts

Scientific Notation

Multiplication of Exponents

Solving for a Variable

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