Laws of indices: rules for powers and roots

7 easy Rules

• Powers and Roots
• 1) When multiplying, ADD the powers
• e.g: 3^6 x 3^4 = 3^10
• 2) When dividing you SUBTRACT the powers
• e.g: 5^4 ÷ 5^2 = 5^2
• 3) When raising one power to the other, MULTIPLY them
• e.g: (3^2)^4= 3^8
• 4) x^1 = x, anything to the power of 1 is ITSELF
• e.g: 3^1 = 3
• 5) x^0 = 1, anything the power of 0 is 1
• e.g: 5^0 = 1
• 6) 1^x= 1 , 1 to the power of any power is still 1
• e.g: 1^23= 1
• 7) FRACTIONS- Apply the powers to both bottom and top
• e.g: (8/5)^3= 8^3/5^3

3 Tricky Rules

• 1) NEGATIVE powers- Turn It Upside Down
• e.g: 7- ^2 = 1/7^2= 1/49
• 2) FRACTIONAL POWERS
• The power 1/2 means Square Root
• The power 1/3 means Cube Root
• The power 1/4 means Fourth Root etc for 5, 6, 7, 8 ...
• 3) TWO STAGE FRACTIONAL POWERS
• e.g: 64^5/6, always split the fraction into a root and a power, and do them in that order: root and then power: (64)^1/6x5 = (64^1/6)^5= 2^5= 32

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