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Further Index laws Theory
![When a term with a power is raised to another power, the powers are multiplied. Any number raised to the power \(0\) is equal to l \begin{multicols}{2} \textbf{Example 1}\\ \(\left(5^3\right)^4 = \)\\ \textbf{Example 1 solution}\\ \(\begin{aligned} \left(5^3\right)^4 & =5^{3 \times 4} \\ & =5^{12} \end{aligned}\)\\ \(\begin{aligned} \text{since } \left(5^3\right)^4 &=5^3 \times 5^3 \times 5^3 \times 5^3\\ & =5^{3+3+3+3} \\ & =5^{12} \end{aligned}\) \columnbreak \textbf{Example 2}\\ \((7)^0=\)\\ \textbf{Example 2 solution}\\ \(\begin{aligned} & (7)^0=1 \end{aligned}\)\\ since \(7 \div 7=1\)\\ and \(\begin{aligned}[t] 7 \div 7 & =7^{1-1} \\ & =7^{\circ} \\ \therefore 7^{\circ} & =1 \end{aligned}\) \end{multicols}](/media/g0ghfopw/29809.png)
NSW Y8 Maths Working with Numbers Further Index laws
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