Numbers and Decimals

Basic Arithmetic

Number Line and Comparing Numbers

Place Value and Rounding Numbers

Basic Arithmetic and Inverse Operations

BIDMAS – Order of Operations

Commutative Property and Associative Property

Distributive Property

Column Addition and Column Subtraction

Long Multiplication

Factors and Multiples

Divisibility and Divisibility Rules

Prime Numbers and Prime Factorization

How to Find HCF and LCM

Powers and Roots

Powers and Indices

Basics of Square Roots

Multiplying and Dividing Square Roots

The nth Root and Fractional Indices

Laws of Indices (Same Base, Same Indices)

Negative Exponents and Power of a Power

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Comparing and Rounding Decimals

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Laws of Indices (Same Base, Same Indices)

Numbers and Decimals Laws of Indices (Same Base, Same Indices)

Courses Overview

🎬 Video Tutorial

(0:01) What are Laws of Indices?: Laws of Indices are rules that simplify calculations involving powers of numbers.
(0:21) Multiplying Indices with Same Base: For multiplication, add the indices ($a^m \times a^n = a^{m+n}$). For example, $2^3 \times 2^4 = 2^{3+4} = 2^7$.
(1:10) Dividing Indices with Same Base: For division, subtract the indices ( $a^m \div a^n = a^{m-n}$). For example, $4^5 \div 4^3 = 4^{5-3} = 4^2$.
(2:02) Multiplying Indices with Same Index: For multiplication, multiply the bases and keep the index ($a^m \times b^m = (a \times b)^m$). For example, $2^3 \times 5^3 = (2 \times 5)^3 = 10^3$.
(2:56) Dividing Indices with Same Index: For division, divide the bases and keep the index ($\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$). For example, $\frac{6^5}{3^5} = \left(\frac{6}{3}\right)^5 = 2^5$.

📂 Revision Cards

Indices example showing 2³ as 2 × 2 × 2, with 2 labelled as base and 3 as index or exponent. — 1) What are Laws of Indices

Laws of indices chart showing rules for multiplying and dividing powers with the same base and same index, with examples for both operations. — 2) Law of Indices Summary

🍪 Quiz Time - Practice Now!

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Laws of Indices (Same Base or Same Indices)

1 / 6

Q: What is $2^3 \times 2^4$ ?

$2^7$

$2^{12}$

$2^6$

$2^8$

Feedback: Not quite! When multiplying numbers with the same base, we add the exponents. The formula used is $a^m \times a^n = a^{m+n}$. So, $2^3 \times 2^4 = 2^{3+4} = 2^7$.

Feedback: Well done! When multiplying numbers with the same base, we add the exponents. The formula used is $a^m \times a^n = a^{m+n}$. So, $2^3 \times 2^4 = 2^{3+4} = 2^7$.

2 / 6

Q: What is $4^5 \div 4^3$ ?

$4^3$

$4^8$

$4^2$

$4^{15}$

Feedback: Not quite! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $4^5 \div 4^3 = 4^{5-3} = 4^2$.

Feedback: Well done! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $4^5 \div 4^3 = 4^{5-3} = 4^2$.

3 / 6

Q: What is $10^5 \div 10^2$ ?

$10^3$

$10^{2.5}$

$10^1$

$10^2$

Feedback: Not quite! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $10^5 \div 10^2 = 10^{5-2} = 10^3$.

Feedback: Well done! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $10^5 \div 10^2 = 10^{5-2} = 10^3$.

4 / 6

Q: Simplify $0.2^5 \times 5^5$.

$(0.2 \times 5)^5$

$1$

$5$

$0.1^5$

Feedback: Not quite! Using the multiplication rule for numbers with the same index $a^n \times b^n = (a \times b)^n$, we get $0.2^5 \times 5^5 = (0.2 \times 5)^5 = 1^5 = 1$.

Feedback: Well done! Using the multiplication rule for numbers with the same index $a^n \times b^n = (a \times b)^n$, we get $0.2^5 \times 5^5 = (0.2 \times 5)^5 = 1^5 = 1$.

5 / 6

Q: Simplify $5^4 \div 5^6$.

$5^0$

$5^{-2}$

$5^2$

$5^{-3}$

Feedback: Not quite! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $5^4 \div 5^6 = 5^{4-6} = 5^{-2}$.

Feedback: Well done! When dividing numbers with the same base, subtract the exponents. The formula is $\frac{a^m}{a^n} = a^{m-n}$. So, $5^4 \div 5^6 = 5^{4-6} = 5^{-2}$.

6 / 6

Q: What is $2^4 \times 2^2 \times 2^3$ ?

$2^{10}$

$2^8$

$2^9$

$2^7$

Feedback: Not quite! When multiplying numbers with the same base, add the exponents. The formula is $a^m \times a^n \times a^p = a^{m+n+p}$. So, $2^4 \times 2^2 \times 2^3 = 2^{4+2+3} = 2^9$.

Feedback: Well done! When multiplying numbers with the same base, add the exponents. The formula is $a^m \times a^n \times a^p = a^{m+n+p}$. So, $2^4 \times 2^2 \times 2^3 = 2^{4+2+3} = 2^9$.

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