课 47, 主题 3

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Laws-Of-Indices Edexcel Foundation

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Exam code:1MA1

Laws of indices

What are the laws of indices?

Index laws are rules you can use when doing operations with powers
- They work with both numbers and algebra

Law	Description	How it works
$a to the power of 1 equals a$	Anything to the power of 1 is itself	$6 to the power of 1 equals 6$
$a to the power of 0 equals 1$	Anything to the power of 0 is 1	$8 to the power of 0 equals 1$
$a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent$	To multiply indices with the same base, add their powers	<img alt=”4 cubed cross times 4 squared equals open parentheses 4 cross times 4 cross times 4 close parentheses cross times open parentheses 4 cross times 4 close parentheses equals 4 to the power of 5″ data-mathml='<math ><semantics><mstyle indentalign=”center”><msup><mn>4</mn><mn>3</mn></msup><mo>×</mo><msup><mn>4</mn><mn>2</mn></msup><mspace linebreak=”newline”></mspace><mo>=</mo><mfenced><mrow><mn>4</mn><mo>×</mo><mn>4</mn><mo>×</mo><mn>4</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mn>4</mn><mo>×</mo><mn>4</mn></mrow></mfenced><mspace linebreak=”newline”></mspace><mo>=</mo><msup><mn>4</mn><mn>5</mn></msup></mstyle><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”76″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2276%22%20width%3D%22155%22%20wrs%3Abaseline%3D%2237%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmstyle%20indentalign%3D%22center%22%3E%3Cmsup%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmsup%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmfenced%3E%3Cmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%26%23xD7%3B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmstyle%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math13d2dc549f508103e95d72be633’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABIWhlYWQQC2qxAAACuAAAADZoaGVhCGsXSAAAAvAAAAAkaG10eE2rRkcAAAMUAAAADGxvY2EAHTwYAAADIAAAABBtYXhwBT0FPgAAAzAAAAAgbmFtZaBxlY4AAANQAAABn3Bvc3QB9wD6AAAE8AAAACBwcmVwa1uragAABRAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACAD0A1%2F%2F%2FAAAAPQDX%2F%2F%2F%2FxP8rAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgADrAtUCFQADAAcAZRgBsAgQsAbUsAYQsAXUsAgQsAHUsAEQsADUsAYQsAc8sAUQsAQ8sAEQsAI8sAAQsAM8ALAIELAG1LAGELAH1LAHELAB1LABELAC1LAGELAFPLAHELAEPLABELAAPLACELADPDEwEyE1IR0BITWAAlX9qwJVAcBV1VVVAAIAgABVAtUCgAADAAcARhiwARQAsQAAExCxAAnksQABExCwBDyxBgj0sAI8MAGxCAETELEAA%2FawBzyxAQX1sAY8sgUHABD0sAI8sQkD5rEEBfWwAzwTMwEjETMBI4BVAgBVVf4AVQKA%2FdUCK%2F3VAAAAAAEAAAABAADVeM5BXw889QADBAD%2F%2F%2F%2F%2F1joTc%2F%2F%2F%2F%2F%2FWOhNzAAD%2FIASAA6sAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%2B2BIAAAQAAAAAAAAAAAAAAAAAAAAMDUgBVA1YAgANWAIAAAAAAAAAAKAAAALIAAAEhAAEAAAADAF4ABQAAAAAAAgCABAAAAAAABAAA3gAAAAAAAAAVAQIAAAAAAAAAAQASAAAAAAAAAAAAAgAOABIAAAAAAAAAAwAwACAAAAAAAAAABAASAFAAAAAAAAAABQAWAGIAAAAAAAAABgAJAHgAAAAAAAAACAAcAIEAAQAAAAAAAQASAAAAAQAAAAAAAgAOABIAAQAAAAAAAwAwACAAAQAAAAAABAASAFAAAQAAAAAABQAWAGIAAQAAAAAABgAJAHgAAQAAAAAACAAcAIEAAwABBAkAAQASAAAAAwABBAkAAgAOABIAAwABBAkAAwAwACAAAwABBAkABAASAFAAAwABBAkABQAWAGIAAwABBAkABgAJAHgAAwABBAkACAA

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