Respuesta :
[tex]\bf \begin{cases}
a^7=7777\\\\ \cfrac{a^6}{b}=11
\end{cases} \\\\
-------------------------------\\\\
a^7\iff a^6a^1=7777\implies
\begin{cases}
a^6=\frac{7777}{a}\\\\
a=\frac{7777}{a^6}
\end{cases}\\\\
-------------------------------\\\\
\cfrac{a^6}{b}=11\implies \cfrac{a^6}{11}=b\implies \cfrac{\frac{7777}{a}}{11}=b\implies \cfrac{7777}{a}\cdot \cfrac{1}{11}=b
\\\\\\
\cfrac{707}{a}=b\\\\
-------------------------------\\\\[/tex]
[tex]\bf a\cdot b=\cfrac{7777}{a^6}\cdot \cfrac{707}{a}\implies ab=\cfrac{7777\cdot 707}{a^6a^1}\implies ab=\cfrac{7777\cdot 707}{a^7} \\\\\\ \textit{but we know }a^7=7777\qquad thus\implies ab=\cfrac{7777}{a^7}\cdot 707 \\\\\\ ab=\cfrac{7777}{7777}\cdot 707\implies ab=1\cdot 707\implies ab=707[/tex]
[tex]\bf a\cdot b=\cfrac{7777}{a^6}\cdot \cfrac{707}{a}\implies ab=\cfrac{7777\cdot 707}{a^6a^1}\implies ab=\cfrac{7777\cdot 707}{a^7} \\\\\\ \textit{but we know }a^7=7777\qquad thus\implies ab=\cfrac{7777}{a^7}\cdot 707 \\\\\\ ab=\cfrac{7777}{7777}\cdot 707\implies ab=1\cdot 707\implies ab=707[/tex]
Answer:
[tex]ab=707[/tex]
Step-by-step explanation:
Given that
[tex]a^7=7777\\[/tex]
[tex]a^6/b=11[/tex]
We have to find the value of ab
WE see that when we divide I equation by II equation we get ab
[tex]\frac{a^7}{\frac{a^6}{b} } =\frac{a^7b}{a^6}[/tex]
by rule for reciprocals
Now use exponent rule for simplifying a terms
[tex]a^{7-6} b =\frac{7777}{11} \\ab=707[/tex]
