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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Simplifying with exponent laws and negative exponents

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 6 s
  • British Columbia
  • BC10-MA-02

The video simplifies (2a³b⁻²)² ÷ (4a⁻¹b) step by step, naming each law as it is used: the power of a product and power of a power laws give 4a⁶b⁻⁴, then the quotient law gives a⁷b⁻⁵. Along the way it shows why 6 − (−1) is 7 and not 5 and checks it by adding back, then uses the negative exponent law to write the answer as a⁷/b⁵ and ends on a one-line recap.

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In one sentence

The question this lesson answers

Let us simplify this expression, and write the answer with positive exponents.

In the power a cubed, a is the base and 3 is the exponent. It means a times a times a.

Transcript

What the lesson says

Let us simplify this expression, and write the answer with positive exponents.

In the power a cubed, a is the base and 3 is the exponent. It means a times a times a.

Step 1 is the square, because exponents come before division.

The bracket multiplies three factors: 2, a cubed and b to the negative 2.

The power of a product law says: square each factor.

2 squared is 2 times 2, which is 4.

For a cubed, squared, the power of a power law says multiply the exponents: 3 times 2 is 6.

For b, negative 2 times 2 is negative 4.

Step 2 is the division. The b on the right has no exponent shown, so its exponent is 1.

The quotient law says: to divide powers with the same base, subtract the exponents.

First the numbers: 4 divided by 4 is 1.

For a, that is 6 minus negative 1.

Subtracting a negative means adding, so 6 plus 1 is 7.

Watch out: 5 is a common mistake here. Check by adding back: 7 plus negative 1 is 6.

For b, negative 4 minus 1 is negative 5.

Multiplying by 1 changes nothing, so we have a to the 7, b to the negative 5.

The negative exponent law says x to the negative n is 1 over x to the n, when x is not 0.

So b to the negative 5 is 1 over b to the 5, and the answer is a to the 7 over b to the 5.

To recap: square each factor, subtract the exponents to divide, then make negative exponents positive.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Number: operations on powers with integral exponentsBC10-MA-02

Previous: Negative exponents: dividing instead of multiplyingNext: Evaluating Powers with the Order of Operations

British Columbia, Grade 11

Pre Calculus 11, Real numbers and powers: powers with rational exponentsBC11-MA-64

Previous: The Real Number System: From Natural Numbers to IrrationalsNext: Rational exponents: a fraction power is a root

This lesson is also listed in Grade 11.

The outcomes and strands follow the British Columbia curriculum.

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