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NSW Y8 Maths

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NSW Y8 Maths Algebra Power of a Power

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Power of a Power Theory

When raising a term with a power to another power, the powers are multiplied together. $$ \begin{aligned} \left(a^m\right)^n & =a^{m \times n} \\ & =a^{m n} \end{aligned} $$ \begin{multicols}{2} \textbf{Example 1}\\ \(\left(3 a^2\right)^3 =\)\\ \textbf{Example 1 solution}\\ \(\begin{aligned} \left(3 a^2\right)^3 & =3^3 \times a^{2 \times 3} \\ & =27 a^6 \end{aligned}\) \columnbreak \textbf{Example 2}\\ \(\left(-2 a^4\right)^3=\)\\ \textbf{Example 2 solution}\\ \(\begin{aligned} \left(-2 a^4\right)^3 & =(-2)^3 \times a^{4 \times 3} \\ & =-8 a^{12} \end{aligned}\) \end{multicols}

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  • Power of a Power - Video - Power of a Power - Example 1

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