Repeated addition is named multiplication.
Similarly, repeated multiplication is named exponents.
• The expression is, to the power of or power .
The special cases where the power is a negative number or a positive fraction are explained.
"Multiplication" is "repeated addition". Multiplication is learned as repeated addition in whole numbers.
is repeated times (or times ).
Later, multiplication is extended to negative numbers and fractions.
eg: is repeated times.
is repeated times.
We learned meaning of multiplication by whole numbers, negative numbers, and fractions.
Similarly, "exponents" are introduced as repeated multiplication.
In this, we learn
• What is exponent to a whole number, eg : ?
• What is exponent to a negative number, eg: ?
• What is exponent to a fraction, eg: ?
The word "exponent" means: a number raised to the power of another number". In plain English, exponent means "higher level or higher order".
base to the power
Exponents : Exponents are repeated multiplication.
is the base
is the exponent or the power
is the result of exponentiation
The word "base" means: the foundation or lower part of something.
The expression is, to the power of or power .
The value of is "".
In the other way, is written as "".
Consider . The power is a negative number. To understand exponent with negative power let us revise the 'integers' (directed numbers).
Integer is in directed whole number form. To compute , in the aligned direction, starting from , multiply in ratio of base .
It progresses in the following order
power is positive, so multiplication is repeated. For a negative power, the inverse of multiplicatio -- "division" -- is repeated.
Integer is in directed whole number form. To compute , in the opposed direction, starting form divide in ratio of base . It progresses in the following order .
In the other way, is written as ""
"exponents" are repeated multiplication.
is the base
is the power
is the exponentiation result
• this is introduced later.
The outline of material to learn "Exponents" is as follows.
Note: click here for detailed outline of Exponents s
→ Representation of Exponents
→ Inverse of exponent : root
→ Inverse of exponent : Logarithm
→ Common and Natural Logarithms
→ Exponents Arithmetics
→ Logarithm Arithmetics
→ Numerical Expressions
→ PEMA / BOMA
→ Squares and Square roots
→ Cubes and Cube roots