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Powers and Number Operations

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Powers and Number Operations

Help Mele check prices, stock and pack sizes using powers, roots and prime factors. Show working where asked. You may use a calculator for the final question.

Powers in action

Use the place-value table to help with Questions 1 and 2.

Power of 10

Value

Example

10²

100

A tray holds 100 apples.

10⁰

One item is one item.

10⁻¹

0.1

One tenth of a dollar is $0.10.

1.A supermarket has 3,450 cans in storage. Write 3,450 in expanded form using powers of 10.

2.A price label shows $0.001 per sample. Write 0.001 as a negative power of 10 and as a fraction.

3.A carton display has 5³ juice boxes. Calculate how many boxes there are.

4.Put these quantities in order from smallest to largest: 10², 10⁻¹, 10⁰. Use the table if helpful.

Roots and factors

Mele is checking stock counts and pack sizes. Use exact values unless told otherwise.

5.A square display has 49 identical packets arranged in equal rows and columns. How many packets are in each row? Write the answer using a square-root symbol.

6.A cube-shaped stack contains 64 small boxes, with the same number along each edge. How many boxes are along one edge? Write the answer using a cube-root symbol.

7.Find the prime factorisation of 72. Write repeated prime factors using exponents.

8.A delivery has 48 snack bars. Express 48 as a product of prime factors using exponents.

Explain and extend

Show your reasoning in the final questions.

9.A stock counter compares 10² items with 10⁴ items. How many times as large is 10⁴ as 10²? Explain using division or powers.

10.A bulk order is written as 2.34 × 10³ items. Write this in standard form, then expand it using powers of 10.

11.Tevita says 10⁰ = 0 because the exponent is zero. Is he correct? Explain why 10⁰ equals its actual value, using a pattern such as 10³, 10², 10¹, 10⁰.

12.The supermarket packs sample sachets in groups of 1,000. Write 0.001 as a power of 10, then calculate √81, ∛27 and √50 to 2 decimal places.