Determine whether each statement is true or false. If false, corr...

Question

Determine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7

Accepted Answer

Hello. Today we're going to be using the properties of exponents to verify whether the given statement is true or false. So what we are given is X to the power of 21 times x to the power of three. And we're going to verify as to whether that is equal to X to the power of 24. Now in order to verify this, we're going to use the property of exponential multiplication And what the property of exponential multiplication states. If you have two exponential values with the same base. So for instance a to the power of X and 8 to the power of Y. If the bases are the same and these quantities are being multiplied by each other then the product is just going to be the same base A But the exponents you're just going to go ahead and add them together. So A to the power of X times A. To the power of Y is equal to a. To the power of X plus Y. And we're going to be applying this property to the left hand side of the statement to verify whether this is true or false. So we have X to the power of 21 times X to the power of three. Both of these exponential values have the same base X. So if we multiply these values together, we're just going to add the exponents together and adding the exponents together is going to give us X to the power of 21 plus three. And that is going to be equal to X. To the power of 24 which matches the right hand side of the given statement, thus verifying that the given statement is true. And since the given statement is true, the answer to this problem is going to be a So I hope this video helps you in understanding how to use this property, and I'll go ahead and see you all in the next video.

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Determine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7