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Multiply the numbers

Answer

Find the number of divisors

Answer

List all divisors

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Do prime factorization

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Organize using the law of exponent

Answer

$531441$

Multiply the numbers

$\color{#FF6800}{ 81 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 } \times 81$

$ $ Multiply $ 81 $ and $ 81$

$\color{#FF6800}{ 6561 } \times 81$

$\color{#FF6800}{ 6561 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 }$

$ $ Multiply $ 6561 $ and $ 81$

$\color{#FF6800}{ 531441 }$

$13$

Find the number of divisors

$\color{#FF6800}{ 81 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 }$

$ $ Do prime factorization $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$ $ Add the exponent as the base is the same $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$3 ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$ $ Find the sum $ $

$3 ^ { \color{#FF6800}{ 12 } }$

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 12 } }$

$ $ Find the number of divisors using an exponent $ $

$\color{#FF6800}{ 13 }$

$1 , 3 , 9 , 27 , 81 , 243 , 729 , 2187 , 6561 , 19683 , 59049 , 177147 , 531441$

Find all divisors

$\color{#FF6800}{ 81 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 } \color{#FF6800}{ \times } \color{#FF6800}{ 81 }$

$ $ Do prime factorization $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$ $ Add the exponent as the base is the same $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$3 ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$ $ Find the sum $ $

$3 ^ { \color{#FF6800}{ 12 } }$

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 12 } }$

$ $ List divisors of factors $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 0 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 3 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 5 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 6 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 7 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 8 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 9 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 10 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 11 } } , \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 12 } }$

$ $ Calculate the product of all divisors $ $

$\color{#FF6800}{ 1 } , \color{#FF6800}{ 3 } , \color{#FF6800}{ 9 } , \color{#FF6800}{ 27 } , \color{#FF6800}{ 81 } , \color{#FF6800}{ 243 } , \color{#FF6800}{ 729 } , \color{#FF6800}{ 2187 } , \color{#FF6800}{ 6561 } , \color{#FF6800}{ 19683 } , \color{#FF6800}{ 59049 } , \color{#FF6800}{ 177147 } , \color{#FF6800}{ 531441 }$

$3 ^ { 12 }$

Organize using the law of exponent

$\color{#FF6800}{ 81 } \times 81 \times 81$

$ $ Represents an integer as a product of decimal numbers $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times 81 \times 81$

$3 ^ { 4 } \times \color{#FF6800}{ 81 } \times 81$

$ $ Represents an integer as a product of decimal numbers $ $

$3 ^ { 4 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times 81$

$3 ^ { 4 } \times 3 ^ { 4 } \times \color{#FF6800}{ 81 }$

$ $ Represents an integer as a product of decimal numbers $ $

$3 ^ { 4 } \times 3 ^ { 4 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } }$

$ $ Add the exponent as the base is the same $ $

$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$3 ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } }$

$ $ Find the sum $ $

$3 ^ { \color{#FF6800}{ 12 } }$

$81 ^ { 3 }$

Organize using the law of exponent

$\color{#FF6800}{ 81 } \times 81 \times 81$

$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $

$\color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } } \times 81 \times 81$

$81 ^ { 1 } \times \color{#FF6800}{ 81 } \times 81$

$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $

$81 ^ { 1 } \times \color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } } \times 81$

$81 ^ { 1 } \times 81 ^ { 1 } \times \color{#FF6800}{ 81 }$

$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $

$81 ^ { 1 } \times 81 ^ { 1 } \times \color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } }$

$\color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } }$

$ $ Add the exponent as the base is the same $ $

$\color{#FF6800}{ 81 } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$

$81 ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$

$ $ Find the sum $ $

$81 ^ { \color{#FF6800}{ 3 } }$

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