Q:

# When 1,250 Superscript three-fourths is written in simplest radical form, which value remains under the radical?2568

Accepted Solution

A:
The value remains under the radical is 8 ⇒ last answerStep-by-step explanation:Let us revise how to write the exponent as a radical$$a^{\frac{m}{n}}$$ can be written as $$\sqrt[n]{a^{m}}$$To simplify the radical factorize the base "a" to its prime factorsExample: $$(54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}$$ , Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 = $$2(3)^{3}$$$$\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}$$2² can not go out the radical because 2 is less than 3 not divisible by 3$$3^{6}$$ can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical$$\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}$$Now let us solve your problem∵ $$1250^{\frac{3}{4}}=\sqrt[4]{1250^{3}}$$- Factorize 1250 to its prime factors∵ 1250 = 2 × 5 × 5 × 5 × 5∴ $$1250=2*5^{4}$$∴ $$\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}$$∵ 2³ can not go out the radical because 3 < 4 and not divisible by it- $$5^{12}$$ can go out the radical because 12 can divided by 4∵ 12 ÷ 4 = 3∴ $$5^{12}$$ can go out the radical as 5³∴ $$\sqrt[4]{1250}=5^{3}\sqrt[4]{2^{3}}$$∴ $$\sqrt[4]{1250}=125\sqrt[4]{8}$$∴ The value remains under the radical = 8The value remains under the radical is 8Learn more:You can learn more about the radicals in brainly.com/question/7153188#LearnwithBrainly