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If 45π₯ to the power π π¦ to the power π plus π and 35π₯ to the power 29 π¦ to the power 32 are like terms, what are the values of π and π?
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In this question, weβre considering like terms.
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If we have two terms that are described as like terms, this means that the exponents of the variables must be equal to each other.
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The coefficients of the numbers that we multiply by can be different.
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So in this case, we can effectively ignore our coefficients 45 and 35 and focus simply on our variables π₯ and π¦.
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So letβs begin by considering our variable π₯.
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If weβre told that theyβre like terms, this means that π₯ to the power of π must be equal to π₯ to the power of 29.
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So since the exponents must be equal, we can then say that π equals 29.
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Iβm moving on for our π¦ variable.
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If theyβre like terms, then π¦ to the power of π plus π must be equal to π¦ to the power of 32.
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And we can put those exponents equal, which means that π plus π must be equal to 32.
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And as weβve already found the value π equals 29, we can substitute that into our equation.
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And in order to find π by itself, we subtract 29 from both sides of the equation, giving us π equals 32 minus 29.
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So π equals three.
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And so, our final answer is π equals 29 and π equals three.