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NSW Y8 Maths Working with Numbers Index laws

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Index laws Theory

When multiplying numbers with the same base, the powers are added.\\ When dividing numbers with the same base, the powers are subtracted. \begin{multicols}{2} \textbf{Example 1}\\ \(7^4 \times 7^2 =\)\\ \textbf{Example 1 solution}\\ \(\begin{aligned} 7^4 \times 7^2 & =7^{4+2} \\ & =7^6 \end{aligned}\)\\ since \(7^4 \times 7^2=(7 \times 7 \times 7 \times 7) \times(7 \times 7)=7^6\) \columnbreak \textbf{Example 2}\\ \(7^4 \div 7^2= \)\\ \textbf{Example 2 solution}\\ \(\begin{aligned} 7^4 \div 7^2&=7^{4-2}\\ &=7^2 \end{aligned}\)\\ \(\begin{aligned} \text { since } 7^4 \div 7^2&=\frac{7 \times 7 \times 7 \times 7}{7 \times 7} \\ & =7 \times 7 \\ & =7^2 \end{aligned}\) \end{multicols}

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Videos relating to Index laws.

  • Index laws - Video - Laws of Indices

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