# Powers

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## Bracket Powers

(3(power of 2))(power of 4)

1) Multiply the powers - 2x4 = 8

(1 3/5)(power of 3)

1) Convert into a top heavy fraction - 8/5

2. Apply the power to both the denominator and the numerator - 8(power of 3) / 5(power of 3)

3. Calcuate - 8(power of 3) = 512

5(power of 3) = 125

= 512/125

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## Negative Powers

7(power of -2)

1) Turn it into a fraction to make the power positive - 1/7

2) Apply the new power to the bottom number - 1/7(power of 2)

3) Calculate the sum on the bottom - 1/49

(3/5)(power of -2)

1) Switch the fractional numbers to make the power positive - (5/3)(power of 2)

2) Apply the new power to both the denominator and the numerator - 5(power of 2) / 3(power of 2)

3) Calculate - 25/9

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## Fractional Powers

If the power is 1/2 = square root the number

If the power is 1/3 = cube root the number

If the power is 1/4 = fourth root the number

49(power of -1/2)

1) Make the number a fraction to turn the power into a positive - 1/49

2) Apply the new power to the bottom number - 1 / 49(square root)

3) Calculate - 1/7

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## Multiplied Fractional Powers

(64)(power 1/6 x5)

1. Put the fractional power into the bracket and leave the other power outside the bracket - (64 (power of 1/6))(power of 5)

2. Calculate the sum inside the bracket - sixth square root of 64 = 2

3. Apply the other power to the new number - (2) (power of 5) = 32

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