when $1,250^{\frac{3}{4}}$ is written in its simplest radical form, which value remains under the…

when $1,250^{\frac{3}{4}}$ is written in its simplest radical form, which value remains under the radical?\n2\n5\n6\n8

when $1,250^{\frac{3}{4}}$ is written in its simplest radical form, which value remains under the radical?\n2\n5\n6\n8

Answer

Explanation:

Step1: Prime - factorize 1250

$1250 = 2\times625=2\times5^4$

Step2: Rewrite the exponent expression

$1250^{\frac{3}{4}}=(2\times5^4)^{\frac{3}{4}}$

Step3: Apply the power - of - a - product rule $(ab)^n=a^n\times b^n$

$(2\times5^4)^{\frac{3}{4}}=2^{\frac{3}{4}}\times(5^4)^{\frac{3}{4}}$

Step4: Apply the power - of - a - power rule $(a^m)^n=a^{mn}$

$(5^4)^{\frac{3}{4}} = 5^{4\times\frac{3}{4}}=5^3$ and $2^{\frac{3}{4}}=\sqrt[4]{2^3}=\sqrt[4]{8}$ So, $1250^{\frac{3}{4}}=5^3\times\sqrt[4]{8}=125\sqrt[4]{8}$

Answer:

D. 8