Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 1 • Question 3

Calculate 3⁴ − 4³. Circle your answer. [A] 17 [B] 145 [C] 0 [D] 24.

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Video Transcript

Calculate three to the power of four minus four to the power of three. Circle your answer: 17, 145, zero, 24.

Both three to the power of four and four to the power of three are using index notation. Let’s take a look at three to the power of four. Three will be considered the base, and four will be considered the index, the power, or the exponent, any of those words. And the way to evaluate these would be to take your base and multiply it to itself the number of times that the index or the power or the exponent says. So three to the power of four means we need to take three times three times three times three, four times essentially.

So we have three times three times three times three. Three times three is nine. Nine times three is 27. And then 27 times three, we take seven times three, which is 21, so we carry the two. Three times two is six, and six plus two gives us eight. So three to the power of four is equal to 81.

Now let’s evaluate four to the power of three. So four is our base; three is our power. So we need to multiply four to itself three times. Four times four is 16. 16 times four, we need take six times four, which is 24, so we carry the two. Four times one is four plus two is six. So four to the power of three is 64. So if we were to take three to the power of four minus four to the power of three, we need to take 81 minus 64, which is 17. Therefore, we circle 17 and that will be our final answer.

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