The simplified expression is [tex]\left(-\frac{5}{7}\right)^{17}[/tex].
Solution:
Given expression is [tex]\left(-\frac{5}{7}\right)^{8} \cdot\left(-\frac{5}{7}\right)^{9}[/tex].
To simplify this expression:
[tex]$\left(-\frac{5}{7}\right)^{8} \cdot\left(-\frac{5}{7}\right)^{9}[/tex]
Using exponent rule:
If the base of the product is same then add the powers of the bases.
[tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]$\left(-\frac{5}{7}\right)^{8} \cdot\left(-\frac{5}{7}\right)^{9}=\left(-\frac{5}{7}\right)^{8+9}[/tex]
[tex]$=\left(-\frac{5}{7}\right)^{17}[/tex]
[tex]$\left(-\frac{5}{7}\right)^{8} \cdot\left(-\frac{5}{7}\right)^{9}=\left(-\frac{5}{7}\right)^{17}[/tex]
The simplified expression is [tex]\left(-\frac{5}{7}\right)^{17}[/tex].
