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Change each expression into radical form and then give the value. No calculators should be necessary. a. 125^(2//3) b. 16^(1//2) c. 16^(-1//2) d. ((1)/(81))^(1//4)

Change each expression into radical form and then give the value. No calculators should be necessary.\newlinea. 1252/3 125^{2 / 3} \newlineb. 161/2 16^{1 / 2} \newlinec. 16−1/2 16^{-1 / 2} \newlined. (181)1/4 \left(\frac{1}{81}\right)^{1 / 4}

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Q. Change each expression into radical form and then give the value. No calculators should be necessary.\newlinea. 1252/3 125^{2 / 3} \newlineb. 161/2 16^{1 / 2} \newlinec. 16−1/2 16^{-1 / 2} \newlined. (181)1/4 \left(\frac{1}{81}\right)^{1 / 4}
  1. Convert to Radical Form: Convert 12523125^{\frac{2}{3}} into radical form.\newlineThe expression 12523125^{\frac{2}{3}} can be rewritten as the cube root of 125125 squared, which is 12523\sqrt[3]{125^2}.
  2. Calculate Value: Calculate the value of 12523125^{\frac{2}{3}}.\newlineSince 125125 is 535^3, we have (53)23\sqrt[3]{(5^3)^2}, which simplifies to 52=255^2 = 25.
  3. Convert to Radical Form: Convert 161216^{\frac{1}{2}} into radical form.\newlineThe expression 161216^{\frac{1}{2}} is the square root of 1616, which is 16\sqrt{16}.
  4. Calculate Value: Calculate the value of 161/216^{1/2}. The square root of 1616 is 44, since 42=164^2 = 16.
  5. Convert to Radical Form: Convert 16−1216^{-\frac{1}{2}} into radical form.\newlineThe expression 16−1216^{-\frac{1}{2}} is the reciprocal of the square root of 1616, which is 116\frac{1}{\sqrt{16}}.
  6. Calculate Value: Calculate the value of 16−1/216^{-1/2}.\newlineSince the square root of 1616 is 44, the reciprocal is 1/41/4.
  7. Convert to Radical Form: Convert (181)14\left(\frac{1}{81}\right)^{\frac{1}{4}} into radical form.\newlineThe expression (181)14\left(\frac{1}{81}\right)^{\frac{1}{4}} is the fourth root of 181\frac{1}{81}, which is 1814\sqrt[4]{\frac{1}{81}}.
  8. Calculate Value: Calculate the value of (181)14\left(\frac{1}{81}\right)^{\frac{1}{4}}. Since 8181 is 343^4, we have 1344\sqrt[4]{\frac{1}{3^4}}, which simplifies to 13\frac{1}{3}.

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