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Formula
Find the number of divisors
$$105 ^ { 2 }$$
$27$
Find the number of divisors
$\color{#FF6800}{ 105 } ^ { 2 }$
 Represents an integer as a product of decimal numbers 
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \right ) ^ { \color{#FF6800}{ 2 } }$
 If the base consists of products of two or more numbers, change to the product of each power 
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } ^ { \color{#FF6800}{ 2 } }$
 Find the number of divisors using an exponent 
$\color{#FF6800}{ 27 }$
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