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Lesson · Grade 9 · Mathematics

Powers: Base, Exponent and Repeated Multiplication

  • Grade 9
  • Mathematics
  • 1 min 50 s
  • British Columbia
  • BC9-MA-05

The video labels the base and the exponent in 2⁷, writes it out as seven 2s multiplied together, and multiplies them left to right, doubling each time to get 2⁷ = 128. It then crosses out the common mistake 2 × 7 = 14 and shows that a variable base works the same way, n⁴ = n × n × n × n, before a one-line recap.

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In one sentence

The question this lesson answers

What does 2 to the power of 7 mean, and what number is it?

This is called a power. A power is a short way to write the same number multiplied again and again.

Transcript

What the lesson says

What does 2 to the power of 7 mean, and what number is it?

This is called a power. A power is a short way to write the same number multiplied again and again.

The large 2 is the base. The base is the number being multiplied.

The small raised 7 is the exponent. Here it tells you how many copies of the base to multiply.

So write the base 7 times, with a times sign between each pair. Count them: 1, 2, 3, 4, 5, 6, 7.

That makes seven 2s, just as the exponent says.

Now multiply from left to right. The product so far doubles each time: 2, 4, 8, 16, 32, 64, 128.

So 2 to the power of 7 equals 128.

A common mistake is to multiply the base by the exponent. That gives 2 times 7, which is 14.

But 2 to the power of 7 means seven 2s multiplied, so it is 128, not 14.

A variable is a letter that stands for a number, and it can be the base too. Here the base is n, and the exponent is 4.

So n to the power of 4 means four n's multiplied: n times n times n times n.

Remember: an exponent like 7 or 4 counts how many copies of the base to multiply. So 2 to the power of 7 is 128.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: exponents and exponent laws with whole-number exponentsBC9-MA-05

Previous: Order of operations with rational numbers and powersNext: Why (−3)² Is Not the Same as −3²

The outcomes and strands follow the British Columbia curriculum.

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