Exponents – Practice Problems

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An exponent is shorthand for the repeated multiplication of a certain number by itself. In exponential notation a^n, a is the base while n is the exponent. The base a is the number which is multiplied n times by itself. For example, instead of writing the very long multiplication expression 2*2*2*2*2*2*2*2, we can write it as 2^8. In this example, 2 is the base while 8 is the exponent. Simplifying 2^8 further gives us 256.

Taking the exponent of a number means raising it to a power where the exponent is the power. The exponential notation 5^4 means raising 5 to the fourth power. A number raised to the second power is said to be squared. Thus, 5^2 is read as 5 squared. On the other hand, a number raised to the third power is said to be cubed. Thus, 4^3 is read as 4 cubed. Incidentally, a perfect square is a number which can be expressed as a square of a certain number while a perfect cube is a number which can be expressed as a cube of a certain number. The number 9 is a perfect square because it is equal to 3^2 while 125 is a perfect cube because it is equal to 5^3.

Some other interesting properties of exponents are that any base raised to 1 is equal to itself and any base raised to zero is equal to 1. Thus, 8^1 equals 8 while 9^0 equals 1.

Be very careful when entering into any agreement involving money or assets used in exponential notations as we must never underestimate the power of exponential growth.

Work with radicals and integer exponents.


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Exercises in this Practice Problem
Explain the expression $2^6$.
Find the right expression for the given example.
Determine the expression describing the total number of cats.
Transform the given expression into exponential form.
Name the parts of the exponential expression $3^2$.
Calculate the given expressions.