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06/10/2022
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What do I need to be able to do? You should be able to: ● ● ● Add/subtract with indices Multiply expressions with indices Divide expressions with indices Know the addition law for indices Know the subtraction law for indices Be familiar with the key results Work with negative exponents HIGHER TIER ONLY Work with fractional exponents power/exponent/index 2 coefficient 5 3d base FRACTIONAL INDICES HIGHER TIER ONLY a = Examples 25²-√25-5 Va a" = (va)" Harder Examples (8 k ²)² = 8³3-³√8-2 Examples 3 25²-(√25) -5³ - 125 Remember that this is the same as (25²) = √81x² = 9x It is really helpful to know the powers of 2 2 4 8 16 32 (9c)² = ( √9+) = (3c²)² = 27c Remember th means we cabe EVERYTHING The brackets (32f) - (√√32f) -(2f")³ = 8fª Refer to the lodder on the right if you're struggling to spot the patterns I Examples II I Examples 5³-5 - 5x5x5 II II || II || 8 Addition Law for Indices axa^=am-n Hy Key Words Base: the number that gets multiplied by a power Power: the number of times the number is used in a multiplication. Exponent: power (see above) Index: power (see above) ● 22 x 23=2x2x2x2x2= 25 • kxk2= kxkxkxkxkxk=k d³d² ● Subtraction Law for Indices 8 means the ● am - a^ = amn Remember this INDICES cube root of 8 Coefficient a number used to multiply a variable Variable: a letter which represents an unknown number Commutative changing the order of the operations doesn't change the result 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. dxdxdxdxd $x NEGATIVE FRACTIONAL INDICES ! EXAMPLE 2 HIGHER TIER ONLY EXAMPLE I I 25 1 I 25 Further Examples 5 Square and Cube Numbers When working with indices, it...
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Alternative transcript:
is helpful to know your square and cube numbers! SQUARE NUMBERS CUBE NUMBERS 2 30 x 40 x 20 -3x4x2xaxaxaxa 125 4w x 5z = 4 x 5 xw x z = 20wz mulply the coefficients Together and then consider the vorables - 24a4 3. (†³)² - 1³ x 1³ 4.3p² x 4p²³-6p4 Don't forget about the order of operations!! 1, 8, 27, 81, 125, 216, 343, 512 =txtxtxtxtxt Remember I this is the same as = Don't forget that if you square something you my by (7x = 2p EXAMPLE 3 (343x) | (343x7 49x⁰ 3px 4p³ 6p4 Remember if there is no power written, it is to the power of Remember best practice to write your varables in phabelcd order ๆ Using the subtraction low,5-4-1 You are expected to know these! Don't forget the order of operations Remember clead of dvding byxcubed we can multiply by the reaprocal 1 49x⁹ Spotting Patterns 3 2 = 2x2x2 = 8 1+1 2² = J = 2x2= 21=2 ↓-1 0 -1 2÷2 21:1 1 2 42 = 2 2² = = = 12/2² 4 2-3 = = = 1/3 4 a in a m #2 axa a 0 KEY THINGS TO REMEMBER Therefore, 2 to the power of 0 is I Remember anything to the power 0 is 1 .m.n. a Each time I add one to the power, I multiply by 2 If we carry this on, we can even say what 2 to the power of a negative number is HIGHER TIER ONLY Va Each time I take, one from the power, I divide by 2 We can even spot that I 2 to the power of -2 is 1 the same as I over 2 to 1 the power of 2 lor 2 squared) -m 1 a ā" a" a" = ath= (Va)"