Question

How could you have simplified problem 7 in a different way?

Answer 1

The simplified form of $(\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}$ is $7^{4} \times 3^{24}$.

Step-by-step explanation:

Here, the given problem is in exponential form with the power of -4.

The question is to simplify $(\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}$

The first step in the simplification process is to multiply the power -4 outside the bracket with each powers inside the bracket.

⇒ $(\frac{7^{12}\times3^{32} }{7^{8}\times3^{8} } )$

Now, split them into two separate terms.

⇒ $(\frac{7^{12} }{7^{8} })$ $(\frac{3^{32} }{3^{8} } )$

We know that, the division in the exponential rule with same base is given by ⇒ $\frac{a^{m} }{a^{n} } = a^{m-n}$

⇒ $7^{12-8}\times 3^{32-8}$

⇒ $7^{4} \times 3^{24}$

Therefore, the simplified form of $(\frac{7^{-3}\times3^{-8} }{7^{-2}\times3^{-2} } )^{-4}$ is $7^{4} \times 3^{24}$.