KS1 (Age 5-7)KS2 (Age 7-11)11 Plus (Age 7-11)KS3 (Age 11-14)GCSE (Age 14-17)PSHE A.I.ESL Spanish Specialist Games

Need help with Level 7-8 Numbers - Indices? Ask our AI Tutor!

AI Tutor - Lucy

Connecting with Tutor...

Please wait while we establish connection

Hi! I'm Lucy, your AI tutor. How can I help you with Level 7-8 Numbers - Indices today?

now

A pond plant doubles its surface area every four days.

Level 7-8 Numbers - Indices

Indices show repeated multiplication. Learn square, cube and negative powers, apply index laws, and use powers of 10 to solve KS3 questions clearly and quickly.

Explore the Topic →

(quiz starts below)

Fascinating Fact:

Indices help describe money growth, since compound interest follows the formula A = P(1 + r)ⁿ, where n is the power of time.

In KS3 Maths, indices (powers) let us write repeated multiplication efficiently and calculate quickly. You’ll apply index laws, use powers of ten, and work confidently with standard form in real contexts.

Key Terms

Index (power): The small number that shows how many times a base is multiplied by itself, e.g., 3⁴ = 3 × 3 × 3 × 3.
Base: The number being repeatedly multiplied, e.g., in 5³ the base is 5.
Standard form: A way to write big or small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Frequently Asked Questions (Click to see answers)

What are the index laws in KS3?

Key rules: a^m × aⁿ = a^m+n, a^m ÷ aⁿ = a^m−n (a ≠ 0), and (a^m)ⁿ = a^mn.

How do zero and negative powers work?

For a ≠ 0, a⁰ = 1. A negative power gives a reciprocal: a⁻ⁿ = 1 / aⁿ; e.g., 2⁻³ = 1/8.

What does 10ⁿ mean in standard form?

It’s a power of ten used to scale numbers. For example, 3.2 × 10⁴ = 32,000 and 5.6 × 10⁻³ = 0.0056.

Try These Related Quizzes

1 .

How many litres will fill a cube of side length 25 cm?

1.25

15.625

25.125

61.25

25³ ÷ 1,000 = 5⁶ ÷ 10³. Remember 1,000 cm³ = 1 litre

2 .

What is 0.2⁴ as a power of 5?

5^-1

5^-2

5^-4

5^-5

0.2 = 1/5 = 5^-1

3 .

What is the result of 16 x 64 as a power of 2?

2⁶

2⁸

2¹⁰

2¹²

16 = 2⁴; 64 = 2⁶; 16 x 64 = 2^{(4 + 6)}

4 .

What is the result of 2⁴ x 8³?

1,992

8,192

65,536

99,664

Convert 8³ to a power of 2 before adding the indices

5 .

How many days are there in 2⁹ x 3³ x 5⁴ seconds?

100

125

Divide by 60 x 60 = 2⁴ x 3² x 5² to find the hours, then divide by 24 = 2³ x 3¹ to find days

6 .

What is the result of dividing 25 by 625?

5¹

5^-1

5²

5^-2

25 = 5²; 625 = 5⁴

7 .

John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?

£168.75

£522.84

£760.44

£1,522.50

After 1 year 500 x 1.015; after 3 years 500 x 1.015³

8 .

What is the result of 2⁷ ÷ 2⁸?

1/2

-1/2

-2

2^{(7 - 8)} = 2^-1 = 1/2 since the negative power is 1 over the positive power

9 .

What index number must follow 3 to give 6,561?

6,561 = 81 x 81 = 3⁴ x 3⁴

10 .

A pond plant doubles its surface area every four days. If it covered an area of 20 cm² on 17^th June, what is its area on 15^th July?

2,560 cm²

2.56 m²

0.256 m²

256 cm²

'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 2⁷

You can find more about this topic by visiting BBC Bitesize - Powers

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

**Unlimited Quizzes Await You! 🚀**

Hey there, quiz champ! 🌟 You've already tackled today's free questions.
Ready for more?

🔓 Unlock UNLIMITED Quizzes and challenge yourself every day. But that's
not all...

🔥 As a Subscriber you can join our thrilling "Daily Streak" against other
quizzers. Try to win a coveted spot on our Hall of Fame Page.

Don't miss out! Join us now and keep the fun rolling. 🎉

Subscribe & Play

**Unlimited Quizzes Await You! 🚀**

Hey there, quiz champ! 🌟 You've already tackled today's free questions. Ready for more?

🔓 Unlock UNLIMITED Quizzes and challenge yourself every day. But that's not all...

🔥 As a Subscriber you can join our thrilling "Daily Streak" against other quizzers. Try to win a coveted spot on our Hall of Fame Page.

Don't miss out! Join us now and keep the fun rolling. 🎉

Subscribe & Play

Contact Details

Education Quizzes

Heron's Way, Wragg Marsh
Spalding
Lincolnshire
PE12 6HH
England

Email

admin@educationquizzes.com

Customer Service

Home Page Parents Students Tutors Teachers
Colour Filters Safe AI
Your Account

Here To Help

About Us

Our Team Testimonials Parent Reviews Terms and Conditions Privacy Policy

Leave Feedback