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Lesson 1: nth Roots, Radicals, and Rational Exponents — Practice Questions

  1. 1. True or false: The first step in solving an equation with a fractional exponent is to isolate the power term.

    • A. True
    • B. False
  2. 2. Solve the equation $x^{3/4} = 4$. Round your answer to two decimal places. Your answer is ___.

  3. 3. Solve the equation for $w$. Round your answer to the nearest thousandth. $1.3w^{0.3} + 4.7 = 5.2$. $w = \_\_\_$

  4. 4. Solve the equation $(3x - 2)^{3/4} = 8$. The value of $x$ is ___.

  5. 5. The incubation time for a bird's egg is given by $I(m) = 12.0m^{0.217}$, where $m$ is the mass in grams. If an egg's incubation time is 26 days, what is its mass? Round to one decimal place. ___ grams.

  6. 6. Solve the equation $3.2x^{0.6} - 9.7 = 8.7$. Round your answer to two decimal places. The value of $x$ is ___.

  7. 7. Solve the equation for $y$. $\frac{2}{3}(2y + 1)^{0.2} = 6$. $y = \_\_\_$

  8. 8. The number of mammal species $M$ is related to the temperature range $R$ by $M = 433.8R^{-0.742}$. If 50 species are found, what is the expected temperature range? Round to the nearest whole degree. ___ degrees Celsius.