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Rational exponents - MYP Questionbank | RevisionDojo

Practice Rational exponents with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Simplify the expression $\left(\frac{1}{64}\right)^{-\frac{1}{3}}$ without using a calculator.

Question 2

Evaluate the following expression without using a calculator: $\left(\frac{1}{4}\right)^{-0.5} + \left(\frac{1}{8}\right)^{-\frac{1}{3}}$

Question 3

Simplify the following expression using exponent laws:

\frac{27^{\frac{2}{3}} \cdot 3^{-1}}{9^{\frac{1}{2}}}

Question 4

Simplify the expression $\sqrt{\frac{x}{\sqrt[3]{x}}}$ and express as a single power of $x$ .

Question 5

Simplify the following expression by converting to a common base:

\frac{\sqrt[3]{9}}{\sqrt{3}}

Question 6

Evaluate the following expression without a calculator:

625^{-0.75}

Question 7

Simplify the product $\sqrt[4]{a} \cdot \sqrt[6]{a}$ as a single radical.

Question 8

Which of the following expressions is NOT mathematically equivalent to $x^{\frac{3}{4}}$ for all $x > 0$ ?

Question 9

For $x > 0$ , the expression $x^{-\frac{2}{5}}$ is equivalent to:

Question 10

Simplify the expression $\frac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}$ and express the result in radical form.

Type

Difficulty

Question 1

Simplify the expression $\left(\frac{1}{64}\right)^{-\frac{1}{3}}$ without using a calculator.

Question 2

Evaluate the following expression without using a calculator: $\left(\frac{1}{4}\right)^{-0.5} + \left(\frac{1}{8}\right)^{-\frac{1}{3}}$

Question 3

Simplify the following expression using exponent laws:

\frac{27^{\frac{2}{3}} \cdot 3^{-1}}{9^{\frac{1}{2}}}

Question 4

Simplify the expression $\sqrt{\frac{x}{\sqrt[3]{x}}}$ and express as a single power of $x$ .

Question 5

Simplify the following expression by converting to a common base:

\frac{\sqrt[3]{9}}{\sqrt{3}}

Question 6

Evaluate the following expression without a calculator:

625^{-0.75}

Question 7

Simplify the product $\sqrt[4]{a} \cdot \sqrt[6]{a}$ as a single radical.

Question 8

Which of the following expressions is NOT mathematically equivalent to $x^{\frac{3}{4}}$ for all $x > 0$ ?

Question 9

For $x > 0$ , the expression $x^{-\frac{2}{5}}$ is equivalent to:

Question 10

Simplify the expression $\frac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}$ and express the result in radical form.

Type

Difficulty

Question 1

Simplify the expression $\left(\frac{1}{64}\right)^{-\frac{1}{3}}$ without using a calculator.

Question 2

Evaluate the following expression without using a calculator: $\left(\frac{1}{4}\right)^{-0.5} + \left(\frac{1}{8}\right)^{-\frac{1}{3}}$

Question 3

Simplify the following expression using exponent laws:

\frac{27^{\frac{2}{3}} \cdot 3^{-1}}{9^{\frac{1}{2}}}

Question 4

Simplify the expression $\sqrt{\frac{x}{\sqrt[3]{x}}}$ and express as a single power of $x$ .

Question 5

Simplify the following expression by converting to a common base:

\frac{\sqrt[3]{9}}{\sqrt{3}}

Question 6

Evaluate the following expression without a calculator:

625^{-0.75}

Question 7

Simplify the product $\sqrt[4]{a} \cdot \sqrt[6]{a}$ as a single radical.

Question 8

Which of the following expressions is NOT mathematically equivalent to $x^{\frac{3}{4}}$ for all $x > 0$ ?

Question 9

For $x > 0$ , the expression $x^{-\frac{2}{5}}$ is equivalent to:

Question 10

Simplify the expression $\frac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}$ and express the result in radical form.

Rational exponents Questionbank