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Lesson · Grade 9 · Mathematics

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

  • Grade 9
  • Mathematics
  • 2 min 20 s
  • British Columbia
  • BC9-MA-08

Starting from base and exponent, the video writes (3²)⁴ out as four copies of 3² to show the answer is 3⁸, so for a power of a power you multiply the exponents, and checks it with 9⁴ = 3⁸ = 6561. It then shows that (5n)³ = 5³ × n³ = 125n³ and (m/n)⁵ = m⁵/n⁵ because the exponent goes to every part inside the brackets, checks the common mistake of writing 5n³ with n = 2 (1000, not 40), and ends on a three-line recap.

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In one sentence

The question this lesson answers

3 squared, or 3 to the power 2, is a power. 3 is the base and 2 is the exponent.

The exponent counts the copies of the base: 3 squared is 3 times 3, which is 9.

Transcript

What the lesson says

3 squared, or 3 to the power 2, is a power. 3 is the base and 2 is the exponent.

The exponent counts the copies of the base: 3 squared is 3 times 3, which is 9.

Put 3 squared in brackets and raise it to the power 4: a power of a power.

That means 4 copies of 3 squared, multiplied together: 1, 2, 3, 4.

Each copy has two threes, and 2 times 4 is 8, so we get 3 to the power 8. Multiply the exponents.

Check: 9 to the power 4 is 6561, and so is 3 to the power 8.

A product is the result of multiplying. 5n means 5 times n, so its factors are 5 and n.

Cubed means to the power 3: 5n in brackets, cubed, is 3 copies of 5n multiplied.

Multiply in any order: put the fives together and the n's together.

That is 5 cubed times n cubed. The exponent goes to every factor inside the brackets.

5 cubed is 5 times 5 times 5, which is 125, so we get 125n cubed.

A common mistake is writing 5n cubed with no brackets. That cubes the n but not the 5.

Check with n equal to 2: 10 cubed is 1000, and 125 times 8 is 1000. But 5 times 8 is 40.

A quotient is the result of dividing. m over n is m divided by n, and n is not zero.

Raised to the power 5, that is 5 copies of m over n, multiplied together.

Multiply the numerators on top and the denominators below: m to the power 5 over n to the power 5.

For a power of a power, multiply the exponents. For a product or quotient, raise every part to the power.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: exponents and exponent laws with whole-number exponentsBC9-MA-08

Previous: Multiplying and Dividing Powers with the Same BaseNext: Why any number to the power 0 is 1

The outcomes and strands follow the British Columbia curriculum.

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