what is the value of the expression $-sqrt3{125^{5}}$?\n$-sqrt3{125^{5}}=square$\n(type an integer or a…

Explanation:

Step1: Rewrite 125 as (5^3)

Since (125 = 5^3), the expression (-\sqrt[3]{125^5}) becomes (-\sqrt[3]{(5^3)^5}). Using the power - of - a - power rule ((a^m)^n=a^{mn}), we have (-\sqrt[3]{5^{15}}).

Step2: Simplify the cube - root

By the property (\sqrt[n]{a^m}=a^{\frac{m}{n}}), for (n = 3) and (m = 15), (\sqrt[3]{5^{15}}=5^{\frac{15}{3}}). So, (-\sqrt[3]{5^{15}}=-5^5).

Step3: Calculate (5^5)

Using the formula (a^n=\underbrace{a\times a\times\cdots\times a}_{n\text{ times}}), (5^5=5\times5\times5\times5\times5 = 3125).

Answer:

(-3125)