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2.02 Evaluating expressions involving powers


We have now looked at exponents and how they can be written in exponential form or expanded form as a product of factors.


A base to the power of any other number, e.g. $3^4$34, can be read as "three to the power of four", and means that the base number is multiplied by itself the number of times shown in the power.


Now we would like to evaluate exponents by actually calculating the product of all of the factors.

The applet below allows us to select a base and an exponent, then see the evaluated product. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.

  1. What is the largest number you can make?
  2. What is the smallest number you can make?
  3. Does the product change more if you slide just the base or just the exponent? Explain.

We may be asked to evaluate just a single power, for example $2^3=8$23=8, or we may be asked to evaluate an expression such as $2^3-3^2$2332. When working with expression, we need to remember our order of operations.

Worked example

Question 1

Evaluate $9^2-2^3$9223 by first rewriting the expression as a product of factors in expanded form.

Think: Exponents tell us how many times we are multiplying a number by itself. We have both exponents and subtraction, so we will need to remember our order of operations.



Original expression

$=$= $9\times9-2\times2\times2$9×92×2×2

Rewriting in expanded form

$=$= $81-8$818

Multiplying the factors

$=$= $73$73




Practice questions


Evaluate $2^6$26.


Evaluate $3^3\times3^2$33×32.


Evaluate $12^2-2^2$12222 .



Write and evaluate numerical expressions involving whole-number exponents.

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