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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Evaluating Powers with the Order of Operations

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 4 s
  • British Columbia
  • BC10-MA-03

Step by step, the video evaluates 3 × 2⁻² + (−4)⁰ − 5², using a card that lists the order of operations and lights up the step being done. Powers come first (2⁻² = 1/4, (−4)⁰ = 1 and not 0, 5² = 25), then multiplication (3 × 1/4 = 3/4), then adding and subtracting from left to right to reach −23 1/4, which is checked with decimals and followed by a one-line recap.

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In one sentence

The question this lesson answers

To evaluate an expression means to work out its value.

It has three powers: 2 to the power negative 2, negative 4 to the power 0, and 5 squared.

Transcript

What the lesson says

To evaluate an expression means to work out its value.

It has three powers: 2 to the power negative 2, negative 4 to the power 0, and 5 squared.

The order of operations: brackets, then powers, then multiplication and division, then addition and subtraction.

The brackets only hold negative 4, so there is nothing to work out inside them.

In 2 to the power negative 2, the base is 2 and the exponent, the small raised number, is negative 2.

Powers come before multiplication, so the exponent belongs only to the 2. Do not multiply 3 by 2 first.

A negative exponent means 1 over the power with a positive exponent. So 2 to the power negative 2 is 1 over 2 squared, or one quarter.

Any number except 0, raised to the power 0, is 1. So negative 4 to the power 0 is 1, not 0.

5 squared means 5 times 5, which is 25. Now every power is replaced by its value.

Next comes multiplication: 3 times one quarter is three quarters.

Last, add and subtract from left to right. Three quarters plus 1 is 1 and three quarters.

Then 1 and three quarters minus 25 is negative 23 and one quarter.

So the expression equals negative 23 and one quarter.

Check with decimals: three quarters is 0.75, and 0.75 plus 1 minus 25 is negative 23.25, the same value.

Remember: brackets, then powers, then multiply and divide, then add and subtract.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Number: operations on powers with integral exponentsBC10-MA-03

Previous: Simplifying with exponent laws and negative exponentsNext: Writing a Prime Factorization with Powers

The outcomes and strands follow the British Columbia curriculum.

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