WEBVTT
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Write an exponential equation in the form π¦ equals π to the power of π₯ for the numbers in the table.
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π₯ equals zero, π¦ equals one.
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π₯ equals one, π¦ equals five.
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π₯ equals two, π¦ equals 25.
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And π₯ equals three, π¦ equals 125.
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There are lots of ways of approaching this question.
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One way would be to substitute the values of π₯ and π¦ into the equation π¦ equals π to the power of π₯.
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Letβs consider the first column when π₯ equals zero, π¦ equals one.
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Substituting in these values gives us one is equal to π to the power of zero.
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We know from our laws of exponents or indices that anything to the power of zero is equal to one.
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Therefore, this doesnβt help us work out the value of π.
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In the next column, weβre told that π₯ is equal to one and π¦ is equal to five.
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This gives us the equation five is equal to π to the power of one.
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Once again, from our laws of exponents, we know that anything to the power of one is equal to itself.
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We can therefore say that if π to the power of one is equal to five, π must be equal to five.
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As we have now calculated the value of π, we can rewrite the exponential equation as π¦ equals five to the power of π₯.
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Whilst this appears to be the correct answer, it is worth substituting in our values in column three and four to check that we are correct.
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Substituting in π₯ equals two gives us π¦ is equal to five squared.
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Squaring a number is the same as multiplying it by itself.
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And five multiplied by five is 25.
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This means that the numbers π₯ equals two and π¦ equals 25 do fit the equation.
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Substituting in π₯ equals three gives us π¦ is equal to five cubed or five to the power of three.
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This is the same as five multiplied by five multiplied by five.
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Five cubed is therefore equal to 125.
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So this pair of numbers also fits the equation.
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We can therefore conclude that the exponential equation π¦ equals five to the power of π₯ is correct.