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MakcuM [25]
2 years ago
12

5^4/5^7 simplified is

Mathematics
2 answers:
Nuetrik [128]2 years ago
5 0

\textbf{Given that,}\\\\~~~\dfrac{5^4}{5^7}\\\\\\=5^{4-7}~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~\dfrac{a^m}{a^n} = a^{m-n}\\\\\\=5^{-3}\\\\\\=\dfrac 1{5^3}~~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~ a^{-n} = \dfrac 1 {a^n},~~~a \neq 0 \\\\\\=\dfrac 1{125}\\\\\\=0.008

Zielflug [23.3K]2 years ago
5 0

Answer:

\frac{1}{125}

Step-by-step explanation:

1.apply \: exponent \: rules :   \frac{ {x}^{a} }{ {x}^{b} }  =   {x}^{a - b}

=  {5}^{4 - 7}

2.subtract \: the \: number : 4 - 7 =  - 3

=  {5}^{ - 3}

3.apply \: exponent \: rule :  {a}^{ - b}  =  \frac{1}{  {a}^{b}  }

=  \frac{1}{ {5}^{3} }

4. \:  {5}^{3}  = 125

=  \frac{1}{125}

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