Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 3 • Question 1

Circle the number that is equivalent to 100 to the power of 4. [A] 1000 [B] 10000 [C] 1000000 [D] 100000000

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Video Transcript

Circle the number that is equivalent to 100 to the power of four. Is it 1000, 10000, 1000000, or 100000000?

Let’s quickly recap on power or index notation. In three to the power of two, the big number three is known as the base. The little number two is the index or the power. The index tells us how many times we multiply the base number by itself. So three squared is three multiplied by three, which is nine. Four to the power of five has a base of four, and an index or a power of five. It’s four times four times four times four times four.

So let’s have a look at 100 to the power of four. Its base is 100, and its power is four. So it’s 100 multiplied by 100 multiplied by 100 multiplied by 100. Let’s deal with the first two 100s. When we multiply by 100, we move the digits to the left two places. We add zeros as placeholders. And that means that 100 multiplied by 100 is 10000. Let’s multiply this by the next 100. That’s 10000 multiplied by 100. We move the digits to the left two spaces, and we add zeros as placeholders. This time it’s 1000000. Finally, we’re going to multiply 1000000 by 100. We move the digits to the left two spaces, and we add placeholders. And that gives us 100000000. 100 to the power of four is 100 000 000.

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