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[tex]$
\text{Solution.} \left(\frac{-4}{3}\right)^7 \times \left(\frac{-4}{3}\right)^8 \div \left(\frac{-3}{4}\right)^5 \text{ is equal to}
$[/tex]

Solution:

Sagot :

GinnyAnsweridn
To find the solution to [tex]\(\left(\frac{-4}{3}\right)^7 \times\left(\frac{-4}{3}\right)^8 \div\left(\frac{-3}{4}\right)^5\)[/tex], follow these steps:

1. Combine like bases using exponent rules:
[tex]\[ \left(\frac{-4}{3}\right)^7 \times \left(\frac{-4}{3}\right)^8 = \left(\frac{-4}{3}\right)^{7+8} = \left(\frac{-4}{3}\right)^{15} \][/tex]

2. Rewrite the entire expression:
[tex]\[ \left(\frac{-4}{3}\right)^{15} \div \left(\frac{-3}{4}\right)^5 \][/tex]

3. Recognize that [tex]\(\left(\frac{-3}{4}\right)^{-1} = \left(\frac{-4}{3}\right)\)[/tex]:
[tex]\[ \left(\frac{-4}{3}\right)^{15} \div \left(\frac{-3}{4}\right)^5 = \left(\frac{-4}{3}\right)^{15} \times \left(\frac{-4}{3}\right)^5 = \left(\frac{-4}{3}\right)^{15-5} = \left(\frac{-4}{3}\right)^{10} \][/tex]

4. Simplify for the base and exponent:
[tex]\[ \left(\frac{-4}{3}\right)^{10} = \left(\frac{-4}{3}\right)^{10} \][/tex]

5. Calculate each part to verify intermediate steps:
- [tex]\(\left(\frac{-4}{3}\right)^7 \approx -74.83091388075754\)[/tex]
- [tex]\(\left(\frac{-3}{4}\right)^5 = \left(-0.2373046875\right)\)[/tex]
- [tex]\(\left(\frac{-4}{3}\right)^{15} \times \left(\frac{-3}{4}\right)^{-5} \approx 315.336855201217\)[/tex]
- [tex]\(\left(\frac{-4}{3}\right)^{10} \approx 17.757726633812588\)[/tex]

The numerical result is:
[tex]\[ \boxed{17.757726633812588} \][/tex]
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