Video: AF5P2-Q01-498141657183

Circle the value of 3⁴. [A] 81 [B] 12 [C] 27 [D] 34?

03:02

Video Transcript

Circle the value of three to the power of four. Is it 81, 12, 27, or 34?

When we raise a number to a power, we need to multiply it by itself that many times. This means that, to calculate three to the power of four, we need to multiply three by three by three by three. There are four threes as the power or index was four. Multiplication is commutative. This means that we can multiply the numbers in any order. Let’s firstly multiply the first two threes. Three multiplied by three is equal to nine. Multiplying the last two threes also gives us nine. We are now left with nine multiplied by nine. This is equal to 81. Therefore, three to the power of four equals 81.

Let’s now check our answer by multiplying the numbers in a different order. Multiplying the first two threes once again gives us nine. So three to the power of four is equal to nine multiplied by three multiplied by three. Nine multiplied by three is equal to 27. So we are left with 27 multiplied by three. Once again, this is equal to 81. 20 multiplied by three is equal to 60. And seven multiplied by three is 21. Adding 60 and 21 gives us an answer of 81. As this is a calculator paper, we could’ve typed the calculation directly into our calculator. We use the power button x with a little square above it, as shown. We could type in three, the power button, then the power four, and then press equals. This would also give us an answer of 81, proving that three to the power of four is 81.

Let’s now look at the three wrong answers and identify some common mistakes. The first incorrect answer is 12. And this is equal to three multiplied by four. This is not the same as three to the power of four. 27 is equal to three cubed as three multiplied by three multiplied by three equals 27. Once again, this is not the same as three to the power of four. The final answer has put the digits three and four together. This is not the same as three to the power of four.

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