    ## Powers on Your Computer's Calculator

 Representing Powers 2³ = 2 · 2 · 2 = 8     The phrase "two to the third power" or "two cubed" has a base of 2, an exponent of 3, and means that 2 is used as a factor 3 times. When math is typed on one line rather than written by hand, 2³ is sometimes written as 2^3 where the caret seperates the base from the exponent so the expression translates as "2 to the 3rd power."     More sophisticated calculators use the following buttons to exponentiate quickly.    Less sophisticated calculators which do not have any of these keys often have features built into the calculator to facilitate quick exponential computation.     Your computer's calculators is one of the less sophisticated types but easily computes integral powers.

The Powers of A Number

Here the contant feature is used to display the powers of a number. • Enter the base,
• Press [x] to multiply,
• Enter the base again,
• Press the [=] again and again counting until the appropriate number of factors is achieved
 Example #1: Powers of two [x][=] is 4,2², 2 to the second power [=] is 8,2³, 2 to the third power [=] is 16,2 to the fourth power [=] is 32,2 to the fifth power, ...   Some of the powers of 2 are 2, 4, 8, 16, 32, ...

 Example #2: Powers of negative three [+/-][x][+/-][=] is 9,(-3)², -3 to the second power [=] is -27,(-3)³, -3 to the third power [=] is 81,-3 to the fourth power [=] is -243,-3 to the fifth power, ...   Some of the powers of -3 are 9, -27, 81, -243, ...

Next, please visit the The Powers of Ten Page and then, Reciprocal's on Your Computer's Calculator.

The Powers of A Number Revisited

Now that you have reviewed the basics through the material above on this page and the Powers of Ten Page, consider the bigger picture.

The constant feature on your calculator permits you, with thought, to compute any integral -- integer type -- power of any base. But, for these below, the calculator is not necessary -- just your thoughts are necessary.

Analyse the next example, fill in the missing info, verify your answer.

 Example #1: Powers of two is , 2 to the negative fourth power is , 2 to the negative third power 1/4 is , 2-to-the-negative-second 1/2 is , 2-to-the-negative-first 1 is , 2-to-the-zero 2 is , 2-to-the-first 4 is 2², 2-to-the-second 8 is 2³, 2-to-the-third 16 is 2-to-the-fourth 32 is 2-to-the-fifth 64 is 2-to-the-sixth • For more of an explanation, press RESTATE.
• Then, continue below.

A Number to-the-Zero. to-the-One, to-the-Negative-One

Three powers of a number are crutial to mental conputation and understanding of more sophisticated concepts such as algebraic computation involving exponents and logs. They are: A Number Raised to 1 Power is That Number.  A Number Raised to 0 Power is One, for all nonzero numbers.  A Number Raised to -1 Power is That Number's Reciprocal, for all nonzero numbers. Though these questions look easy, THIS IS A VERY DIFFICULT SET OF QUESTIONS!

 Q1: What's the reciprocal of the reciprocal of the reciprocal of four?
 Q2: Simplify: Q3: Simplify: Q4: Simplify: Q5: Simplify:      This page is brought to you by MATHEMATICAL CONCEPTS, inc., publishers of MATH SPOKEN HERE!, ISBN: 0-9623593-5-1.

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