Planning tool

Students:

• expand skill with exponent laws
• recognise how to expand and simplify numeric and algebraic expressions involving exponents
• know how to apply exponent laws to simplify expressions.

Some students may:

• multiply, rather than add, the exponents when simplifying exponential expressions involving multiplication.
• divide, rather than subtract the exponents when simplifying exponential expressions involving division.
• not realise that a pronumeral without the exponent showing always has an exponent of 1; that is 2 = 2¹, x = x¹.
• not realise that base integers with an exponent of 0 equals 1, 3⁰ = 1, x⁰ = 1.

Use the expansion of exponents for students to make connections between notation and their actual representation and meaning. Encourage students to show the exponent step in their working to show they understand. Continue to develop the simplification and solving of more complex algebraic problems involving exponents.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning about the application of exponential notation in computer storage units.
• We are learning about writing common computer storage bytes in exponent form using 1024 as the base in an equivalent form.

Why are we learning about this?

Exponential notation is used to express numbers or variables that are repeatedly being multiplied by themselves in a more concise and manageable way. Computer programmers, engineers, scientists, economists, actuaries are some of the people who use exponential notation in their everyday working life.

What to do

1. Write the following two exponential numbers out in full:

• Gigabyte (GB): 1024³ = _____________________________ bytes
• Terabyte (TB) = 1024⁴ = ___________________________________ bytes

     Imagine writing these numbers out in full every time you needed to use them!

2. Which one of the following two statements is correct, A or B?

• A: Gigabyte + 1024 = Terabyte
• B: Gigabyte × 1024 = Terabyte

     Hint: look at the exponent laws for help.

3. A kilobyte (KB) is 1024 bytes. A kilobyte can also be expressed in exponent form using 2 as the base:
1024 = 2¹⁰.

   Write the following storage bytes in exponent form using 2 as the base:

• Megabyte (MB) 1024²
• Petabyte (PB) 1024⁵
• Yottabyte (YB) 1024⁸

Success criteria

• I can write an equation that relates one computer storage unit to another.
• I can rewrite a common computer storage unit as an equivalent exponent using 2 as the base.