How to Move an Exponent to the Other Side

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Moving the exponent to the other side isn't something that can be done without making other adjustments. Move an exponent to the other side with help from an experienced educator in this free video clip.

Part of the Video Series: Math Made Easy
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Video Transcript

Hi, my name is John Coder, and I'm a math consultant with Faith Christian Academy in Arvada, Colorado. We're going to take a look at how to move an exponent to the other side of an equation. We have two examples of equations up here with exponents. The first example we have is x-squared equals 64. To remove the x-squared, we need to take the square root of both sides. So I take the square root of x-squared, equals the square root of 64. Now when you take the square root of x-squared, you come up with the absolute value of x. This square root of 64 is 8, because 8 times 8 equals 64. To solve an absolute value equation, we need to think of two different numbers that go in for x, that results in a positive 8. Well the two values would be x equals 8, or negative 8. We can check our work by plugging in the value 8 in for x. So then we have 8-squared, 8 times 8, equals 64. Similarly, with negative 8, if we take negative 8 times negative 8, two negatives make a positive when you multiply, we get positive 64. Let's take a look at the other example, which has an exponent of 3. Now this time, we're going to take the cube root of 3 on both sides of the equation. Now since 3 is an odd number, and we take a cube root, on both sides of the equation, we do not result with absolute values. Instead, we're going to have just x minus 4 on the left side, and on the right side, the cube root of 125 is 5. The next step is to get x by itself by getting rid of a minus 4. We want to do the opposite, so we are going to add 4 on both sides, add the equations down, the minus 4 plus 4 drop out, and we're left with x equals 5 plus 4, which is 9. We can plug this value back into the original equation to get 9 minus 4, which is 5, 5 raised to the third power is 125. My name is John Coder, I'm a math consultant with Faith Christian Academy in Arvada, Colorado, and we just learned how to move an exponent to the other side of an equation. Thank you for watching.

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