Equations with Rational Exponents (Grade 12 NSC Matric Mathematics): Quizzes

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Equations with Rational Exponents
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In a rational exponent xm/nx^{m/n}, what does the denominator nn represent?

The root to be taken

In a rational exponent xm/nx^{m/n}, what does the numerator mm represent?

The power to raise to

What is the value of 82/38^{2/3}?

44

How is x34\sqrt[4]{x^3} written in exponential form?

x3/4x^{3/4}

To solve x2/3=8x^{2/3} = 8, what power should both sides be raised to?

32\frac{3}{2}

What is the solution to x2/5=32x^{2/5} = 32?

x=40962x = 4096\sqrt{2}

When should you consider both positive and negative solutions?

When dealing with even exponents

What is the solution to x23=27\sqrt[3]{x^2} = 27?

x=±813x = \pm 81\sqrt{3}

What is a critical mistake to avoid with rational exponent equations?

Forgetting ± solutions for even exponents

When are negative bases with even roots undefined?

In real numbers

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