Understand and use the laws of indices for all rational exponents.
"Index" (plural: "indices") and "exponent" mean the same thing as "power".
The laws of indices:
- \(a^x×a^y=a^{x+y}\)
- \(a^x÷a^y=a^{x-y}\)
- \((a^x)^y=a^{xy}\)
- \((ab)^y=a^xb^x\)
Fractional and negative powers:
- \(a^{\frac{1}{y}}=\sqrt[y]{a}\)
- \(a^{\frac{x}{y}}=\sqrt[y]{a^x}\)
- \(a^{-x}=\dfrac{1}{a^x}\)
Also remember:
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