The simplified form of [tex](\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}[/tex] is [tex]7^{4} \times 3^{24}[/tex].
Step-by-step explanation:
Here, the given problem is in exponential form with the power of -4.
The question is to simplify [tex](\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}[/tex]
The first step in the simplification process is to multiply the power -4 outside the bracket with each powers inside the bracket.
⇒ [tex](\frac{7^{12}\times3^{32} }{7^{8}\times3^{8} } )[/tex]
Now, split them into two separate terms.
⇒ [tex](\frac{7^{12} }{7^{8} })[/tex] [tex](\frac{3^{32} }{3^{8} } )[/tex]
We know that, the division in the exponential rule with same base is given by ⇒ [tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]
⇒ [tex]7^{12-8}\times 3^{32-8}[/tex]
⇒ [tex]7^{4} \times 3^{24}[/tex]
Therefore, the simplified form of [tex](\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}[/tex] is [tex]7^{4} \times 3^{24}[/tex].
