Directions: In 1 whole paper, COPY and rewrite the following radical expressions into rational exponents (1) \( \sqrt{10} \) (0) \( 8 \sqrt[4]{b^{8} e^{12} r^{7}} \) (2) \( \sqrt[5]{c^{2}} \) (7) \( \sqrt{15 x^{9} m^{6}} \) (3) \( 2 \sqrt[3]{y^{7}} \) (8) \( \sqrt[3]{27 b^{6}} \) (4) \( \sqrt{64 a^{12}} \) (9) \( \sqrt[8]{z^{32}} \) (5) \( \sqrt{81 m^{10} n^{5}} \) (1) \( \sqrt[10]{n^{20} a^{10} y^{30} r^{50}} \)
Added by Eric V.
Close
Step 1
(0) \( 8 \sqrt[4]{b^{8} e^{12} r^{7}} \) can be rewritten as \( 8(b^{8} e^{12} r^{7})^{1/4} \). (2) \( \sqrt[5]{c^{2}} \) can be rewritten as \( c^{2/5} \). (7) \( \sqrt{15 x^{9} m^{6}} \) can be rewritten as \( (15 x^{9} m^{6})^{1/2} \). (3) \( 2 Show moreβ¦
Show all steps
Your feedback will help us improve your experience
Gregory Higby and 86 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Write with a rational exponent. (a) $\sqrt[4]{5 x}$ (b) $\sqrt[8]{9 y}$ (c) $7 \sqrt[5]{3 z}$
Roots and Radicals
Simplify Rational Exponents
In the following exercises, write with a rational exponent. (a) $\sqrt[8]{r}$ (b) $\sqrt[12]{5}$ (c) $\sqrt[4]{t}$
Rational Exponents
Write the expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers. Example: $\sqrt[15]{x^{10}} \quad \frac{\text { Rational }}{\text { exponents }} \quad x^{10 / 15} \quad \stackrel{\text { Simplify }}{\longrightarrow}$ $x^{2 / 3} \quad \frac{\text { Radical }}{\text { notation }} \quad \sqrt[3]{x^{2}}$ $$\sqrt[6]{x^{3} y^{6}}$$
Radicals and Complex Numbers
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD