Respuesta :

Answer and Step-by-step explanation:

2 * 2 * 2 * 2 * 2 * 2 * 2 = 128

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1024

4 * 4 * 4 * 4 * 4 = 1024

8 * 8 = 64

[tex]\frac{128 - 1024}{1024 - 64}[/tex]

[tex]\frac{-896}{960}[/tex]

896 and 960 both have 64 in common.

896 divided by 64 equals 14.

960 divided by 64 equals 15.

[tex]-\frac{14}{15}[/tex] is the answer.

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Step-by-step explanation:

[tex]\longrightarrow\sf \dfrac {2^7-2^10}{4^5-8^2}[/tex]

  • Substitute the values

[tex]\longrightarrow\sf \dfrac {128-1024}{1024-64}[/tex]

[tex]\longrightarrow\sf \dfrac {-896}{960}[/tex]

[tex]\longrightarrow\sf \dfrac {-14}{15}[/tex]

More to know:-

Laws of exponents:-

[tex]\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}[/tex]

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