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Lesson · Grade 9 · Mathematics

Why any number to the power 0 is 1

  • Grade 9
  • Mathematics
  • 2 min 6 s
  • British Columbia
  • BC9-MA-09

Using 6 as the worked example, the video names the base and the exponent and builds a table where each step down (6³ = 216, 6² = 36, 6¹ = 6) divides by 6, so 6⁰ = 6 ÷ 6 = 1; along the way it shows m¹ = m and crosses out the common mistake 6⁰ = 0. It then confirms the result with the rule for dividing powers (y³ ÷ y³ = y³⁻³ = y⁰, and a number divided by itself is 1, checked with 216 ÷ 216 = 1) and ends on the recap y⁰ = 1 for any number y except 0.

Concept: Why any number to the power zero is 1

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In one sentence

The question this lesson answers

What is 6 to the power 0? Let us work it out.

In 6 to the power 3, 6 is the base and 3 is the exponent.

Transcript

What the lesson says

What is 6 to the power 0? Let us work it out.

In 6 to the power 3, 6 is the base and 3 is the exponent.

The exponent says how many sixes to multiply: 6 times 6 times 6 is 216.

Lower the exponent by 1. 6 to the power 2 is 6 times 6, which is 36.

That is one 6 fewer, so we divide by 6. 216 divided by 6 is 36.

Lower it again. 6 to the power 1 is just one 6, and 36 divided by 6 is 6.

In the same way, for any number m, m to the power 1 is just m.

Now one more step, to 6 to the power 0. Keep the pattern and divide by 6 again.

6 divided by 6 is 1. So 6 to the power 0 is 1.

A common mistake is to say 6 to the power 0 is 0. The pattern shows it is 1.

Here is another way. Let y stand for a number. To divide powers of y, subtract the exponents.

3 minus 3 is 0, so y to the power 3 divided by y to the power 3 is y to the power 0.

But a number divided by itself is 1, as long as it is not 0. So this same division is also 1.

Check with y equal to 6. 6 to the power 3 is 216, and 216 divided by 216 is 1.

Both lines start with the same division, so y to the power 0 equals 1.

So any number except 0, raised to the power 0, equals 1.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: exponents and exponent laws with whole-number exponentsBC9-MA-09

Previous: Power of a power, and power of a product or quotient

The outcomes and strands follow the British Columbia curriculum.

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