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Lesson · Grade 9 · Mathematics

Why (−3)² Is Not the Same as −3²

  • Grade 9
  • Mathematics
  • 2 min 1 s
  • British Columbia
  • BC9-MA-06

The brackets in (−3)² make −3 the base, so (−3) × (−3) = 9, while in −3² only the 3 is squared and the negative sign goes on last, giving −9. The video then shows that (−2)³ = −8 and (−2)⁴ = 16, so a negative base gives a negative answer with an odd exponent and a positive one with an even exponent, and warns that typing −3² into a calculator without brackets gives −9, not 9.

Concept: Why (-3) squared is not the same as -3 squared

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In one sentence

The question this lesson answers

These two look almost the same: negative 3 in brackets, squared, and negative 3 squared. Are they equal?

Each one is a power. The base is the number being multiplied, and the small raised 2 is the exponent: it says to multiply two copies of the base.

Transcript

What the lesson says

These two look almost the same: negative 3 in brackets, squared, and negative 3 squared. Are they equal?

Each one is a power. The base is the number being multiplied, and the small raised 2 is the exponent: it says to multiply two copies of the base.

Both exponents are 2. So which number is the base in each one?

In the first, the brackets hold the negative sign and the 3 together, so the base is negative 3.

Negative 3 times negative 3 is 9, because a negative times a negative is a positive.

The second has no brackets, so the exponent belongs only to the 3. The base is just 3.

Square the 3 first: 3 times 3 is 9. The negative sign goes on last, giving negative 9.

So they are not equal: one is 9, the other is negative 9.

Now negative 2 in brackets, cubed: three copies of negative 2. The first two make 4, and 4 times negative 2 is negative 8.

To the power of 4, use four copies. Each pair makes 4, and 4 times 4 is 16.

With a negative base, an even exponent gives a positive answer, and an odd exponent gives a negative answer.

A common mistake is typing negative 3 squared, without brackets, into a calculator and expecting 9. Most scientific calculators show negative 9.

To square negative 3, type the brackets. Then you get 9.

Remember: the brackets decide the base. Negative 3 in brackets, squared, is 9, but negative 3 squared is negative 9.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: exponents and exponent laws with whole-number exponentsBC9-MA-06

Previous: Powers: Base, Exponent and Repeated MultiplicationNext: Multiplying and Dividing Powers with the Same Base

The outcomes and strands follow the British Columbia curriculum.

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