Question

what is the value of the expression $-sqrt3{125^{5}}$?
$-sqrt3{125^{5}}=square$
(type an integer or a decimal.)

Explanation:

Step1: Rewrite 125 as a power of 5

$125 = 5^3$

Step2: Substitute into the radical

$-\sqrt[3]{(5^3)^5}$

Step3: Simplify the exponent inside

$(5^3)^5 = 5^{3\times5}=5^{15}$

Step4: Simplify the cube root

$\sqrt[3]{5^{15}} = 5^{\frac{15}{3}}=5^5$

Step5: Calculate $5^5$ and apply the negative sign

$5^5=3125$, so $-5^5=-3125$

Answer:

$-3125$