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Lesson · Grade 9 · Mathematics

Multiplying and Dividing Powers with the Same Base

  • Grade 9
  • Mathematics
  • 2 min 7 s
  • British Columbia
  • BC9-MA-07

Writing n⁵ × n³ out as eight n's shows why we keep the base and add the exponents to get n⁸, and a check with numbers confirms 2³ × 2² = 8 × 4 = 2⁵ = 32. Cancelling three pairs in y⁷ ÷ y³ leaves y⁴, so dividing subtracts the exponents. The video then shows two common mistakes: multiplying the exponents (n¹⁵) and using the law with different bases (2³ × 3² is 72, not 6⁵ = 7776).

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In one sentence

The question this lesson answers

How do we multiply n to the power of 5 by n to the power of 3?

In n to the power of 5, n is the base and 5 is the exponent. The whole thing is a power.

Transcript

What the lesson says

How do we multiply n to the power of 5 by n to the power of 3?

In n to the power of 5, n is the base and 5 is the exponent. The whole thing is a power.

The exponent counts how many times the base is a factor: n to the power of 5 is five n's, and n to the power of 3 is three.

Count them: 1, 2, 3, 4, 5, 6, 7, 8. That makes n to the power of 8.

This is an exponent law: to multiply powers with the same base, keep the base and add the exponents. 5 plus 3 is 8.

Check with numbers: 2 to the power of 3 times 2 to the power of 2 is 8 times 4, or 32. Adding the exponents gives 2 to the power of 5, also 32.

Now divide y to the power of 7 by y to the power of 3: seven y's on top, three y's on the bottom.

Since y divided by y is 1 when y is not zero, we cancel three pairs: 1, 2, 3.

Four y's are left on top, so the answer is y to the power of 4.

To divide powers with the same base, keep the base and subtract the exponents. 7 minus 3 is 4.

A common mistake is to multiply the exponents, 5 times 3, and get n to the power of 15. We add them: 5 plus 3 is 8.

The law needs the same base: 2 to the power of 3 times 3 to the power of 2 is 72, not 6 to the power of 5, which is 7776.

Recap: with the same base, multiplying powers adds the exponents, and dividing powers subtracts them.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Number: exponents and exponent laws with whole-number exponentsBC9-MA-07

Previous: Why (−3)² Is Not the Same as −3²Next: Power of a power, and power of a product or quotient

The outcomes and strands follow the British Columbia curriculum.

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