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Find the number of divisors
Answer
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Do prime factorization
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$36 ^{ 19 }$
$1521$
Find the number of divisors
$\color{#FF6800}{ 36 } ^ { 19 }$
$ $ Represents an integer as a product of decimal numbers $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { 19 }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$ $ If the base consists of products of two or more numbers, change to the product of each power $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } } \left ( 3 ^ { 2 } \right ) ^ { 19 }$
$ $ Calculate the power of the power $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 38 } } \left ( 3 ^ { 2 } \right ) ^ { 19 }$
$2 ^ { 38 } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$ $ Calculate the power of the power $ $
$2 ^ { 38 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 38 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 38 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 38 } }$
$ $ Find the number of divisors using an exponent $ $
$\color{#FF6800}{ 1521 }$
$2 ^ { 38 } \times 3 ^ { 38 }$
Organize using the law of exponent
$\color{#FF6800}{ 36 } ^ { 19 }$
$ $ Represents an integer as a product of decimal numbers $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { 19 }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$ $ If the base consists of products of two or more numbers, change to the product of each power $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } } \left ( 3 ^ { 2 } \right ) ^ { 19 }$
$ $ Calculate the power of the power $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 38 } } \left ( 3 ^ { 2 } \right ) ^ { 19 }$
$2 ^ { 38 } \left ( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 19 } }$
$ $ Calculate the power of the power $ $
$2 ^ { 38 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 38 } }$
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