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Formula
Find the number of divisors
$$15 \times 15$$
$9$
Find the number of divisors
$\color{#FF6800}{ 15 } \color{#FF6800}{ \times } \color{#FF6800}{ 15 }$
 Do prime factorization 
$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 3 } \times 3 \times 5 \times 5$
 If the exponent is omitted, the exponent of that term is equal to 1 
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 3 \times 5 \times 5$
$3 ^ { 1 } \times \color{#FF6800}{ 3 } \times 5 \times 5$
 If the exponent is omitted, the exponent of that term is equal to 1 
$3 ^ { 1 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 \times 5$
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 \times 5$
 Add the exponent as the base is the same 
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \times 5 \times 5$
$3 ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \times 5 \times 5$
 Add $1$ and $1$
$3 ^ { \color{#FF6800}{ 2 } } \times 5 \times 5$
$3 ^ { 2 } \times \color{#FF6800}{ 5 } \times 5$
 If the exponent is omitted, the exponent of that term is equal to 1 
$3 ^ { 2 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \times 5$
$3 ^ { 2 } \times 5 ^ { 1 } \times \color{#FF6800}{ 5 }$
 If the exponent is omitted, the exponent of that term is equal to 1 
$3 ^ { 2 } \times 5 ^ { 1 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } }$
$3 ^ { 2 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } }$
 Add the exponent as the base is the same 
$3 ^ { 2 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$3 ^ { 2 } \times 5 ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
 Add $1$ and $1$
$3 ^ { 2 } \times 5 ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } }$
 Find the number of divisors using an exponent 
$\color{#FF6800}{ 9 }$
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