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Calculate the value
Answer
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Find the number of divisors
Answer
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Do prime factorization
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$200 ^{ 2 }$
$40000$
Calculate the value
$\color{#FF6800}{ 200 } ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate power $ $
$\color{#FF6800}{ 40000 }$
$35$
Find the number of divisors
$\color{#FF6800}{ 200 } ^ { 2 }$
$ $ Represents an integer as a product of decimal numbers $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ If the base consists of products of two or more numbers, change to the product of each power $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \left ( 5 ^ { 2 } \right ) ^ { 2 }$
$ $ Calculate the power of the power $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 6 } } \left ( 5 ^ { 2 } \right ) ^ { 2 }$
$2 ^ { 6 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate the power of the power $ $
$2 ^ { 6 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 6 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } }$
$ $ Find the number of divisors using an exponent $ $
$\color{#FF6800}{ 35 }$
$2 ^ { 6 } \times 5 ^ { 4 }$
Organize using the law of exponent
$\color{#FF6800}{ 200 } ^ { 2 }$
$ $ Represents an integer as a product of decimal numbers $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ If the base consists of products of two or more numbers, change to the product of each power $ $
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \left ( 5 ^ { 2 } \right ) ^ { 2 }$
$ $ Calculate the power of the power $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 6 } } \left ( 5 ^ { 2 } \right ) ^ { 2 }$
$2 ^ { 6 } \left ( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate the power of the power $ $
$2 ^ { 6 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } }$
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