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Suppose we have the repeated multiplication
$8\cdot 8\cdot 8\cdot 8\cdot 8$
Write the following multiplication using exponents.
$3\cdot 3$ . Since the factor 3 appears 2 times, we record this as
${3}^{2}$
$\text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}$ . Since the factor 62 appears 9 times, we record this as
${\text{62}}^{9}$
Expand (write without exponents) each number.
${\text{12}}^{4}$ . The exponent 4 is recording 4 factors of 12 in a multiplication. Thus,
${\text{12}}^{4}=\text{12}\cdot \text{12}\cdot \text{12}\cdot \text{12}$
${\text{706}}^{3}$ . The exponent 3 is recording 3 factors of 706 in a multiplication. Thus,
${\text{706}}^{3}=\text{706}\cdot \text{706}\cdot \text{706}$
Write the following using exponents.
$\text{16}\cdot \text{16}\cdot \text{16}\cdot \text{16}\cdot \text{16}$
${\text{16}}^{5}$
$9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9$
${9}^{\text{10}}$
Write each number without exponents.
$\mathrm{1,}{\text{739}}^{2}$
$\mathrm{1,}\text{739}\cdot \mathrm{1,}\text{739}$
In a number such as ${8}^{5}$ ,
5 to the second power, or
5 to the second, or
5 squared.
5 to the third power, or
5 to the third, or
5 cubed.
When a whole number is raised to the power of 4 or higher, we simply say that that number is raised to that particular power. The number ${5}^{8}$ can be read as
5 to the eighth power, or just
5 to the eighth.
In the English language, the word "root" can mean a source of something. In mathematical terms, the word "root" is used to indicate that one number is the source of another number through repeated multiplication.
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