Introduction to Powers:

Powers, also known as exponents, are a way to shorten long strings of multiplication.

Instead of writing 5 x 5 x 5 x 5, write 5^4 which means "multiply four 5s together."

Or how about this for a timesaver: isn't 10^9 easier to write than 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10?

Important Rules of Powers

  1. Any number to the power of 0 is 1
    • 25^0 = 1 and 0.02764187^0=1
  2. Any number to the power of 1 is itself
    • 5^1= 5 and -(218)^1 = -218
  3. When you see a number raised to a negative exponent, take the reciprocal of the number (flip the fraction) and then change the exponent from negative to positive 
    • 2^-3 - (1 / 2)^3 - 1 / 8
  4. Remember to follow PEMDAS, the order of operations-6^2 and (-6)^2 are two different problems. 
    • The first, -6^2 , means to take the negative of 6^2. The answer is the negative of 36 or -36
    • The second problem means to square -6, so it would simplify as -6 x -6, or 36

Powers Practice:

Powers Example 1

2^4 + 5^0


Powers Example 2

-10^1 x 8^2


Powers Example 3

(-4)^3 / 4^2


Powers Example 4

(2/3)^-2


Powers Example 5

(-5)^2 + -5^2 + -5^0 + (-5)^1


Powers Example 6

10^-3 + 0.006


Powers Exercise 1

(5 + 83 - 237)^0


Powers Exercise 2

(-15)^2 + 1^5


Powers Exercise 3

(5/6)^-1


Powers Exercise 4

5(2 + -4)^3


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