# Powers and roots

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• Created by: connor27
• Created on: 29-11-15 20:15
• Powers and roots
• Rule 1: When multiplying, you add the powers.
• e.g. 3 to the power of 4 x 3 to the power of 6 = 3 to the power of 10.
• Rule 2: When dividing, you subtract the powers.
• e.g. 5 to the power of 4 divided by 5 to the power of 2 = 5 to the power of 2.
• Rule 3: When raising one power to another, you multiply them.
• e.g. (3 to the power of 2) to the power of 4 = 3 to the power of 8
• Rule 4: Anything to the power of 1 is itself.
• e.g. 3 to the power of 1 = 3
• Rule 5: Anything to the power of 0 = 1.
• e.g. 5 to the power of 0 = 1.
• Rule 6: 1 to any power is just 1.
• e.g. 1 to the power of 23 = 1.
• Rule 7: With fractions apply the power to both the bottom and top
• e.g. (1 3/5) to the power of 3 = (8/5) to the power of 3 = 8 to the power of 3/5 to the power of 3 = 512/125.
• Rule 8: When the power is negative you need to turn it the other way up.
• e.g. 7 to the power of -2 = 1/7 to the power of 2 = 1/49
• Rule 9: The power 1/2 means square root, the power 1/3 means cube root and the power 1/4 means fourth root etc.
• e.g. 64 to the power of 1/3 = cube root 64 = 4.
• Remember, if the fractional power is negative it needs to be flipped.
• Rule 10: With fractional powers like 64 to the power of 5/6, always split the fraction into root and power.
• e.g. 64 to the power of 5/6 = (64)to the power of 1/6 x 5 = (2) to the power of 5 = 32.