Basic Mathematics

# Rational Exponents

Simplify $\left( 5^{1/6} \right)^{6/4}$.

Evaluate $\sqrt[3]{2 ^{3} \times 2 ^3}.$

Evaluate $\large \left[ \left(\frac{1}{3}\right)^{-\frac{4}{3}} \right]^{\frac{3}{2}} \times 9 ^{-1}.$

What is the value of $a$ that satisfies $\left(\sqrt{7}\right)^{4} \times \left(\sqrt[3]{7}\right)^{3} =7 ^a?$

Which of the following is equivalent to $5^{-\frac{1}{4}}$?

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The text passage contains multiple mathematical questions involving rational exponents and their simplification or evaluation. No answers are provided for these questions.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Basic Mathematics

# Rational Exponents

Simplify $\left( 5^{1/6} \right)^{6/4}$.

Evaluate $\sqrt[3]{2 ^{3} \times 2 ^3}.$

Evaluate $\large \left[ \left(\frac{1}{3}\right)^{-\frac{4}{3}} \right]^{\frac{3}{2}} \times 9 ^{-1}.$

What is the value of $a$ that satisfies $\left(\sqrt{7}\right)^{4} \times \left(\sqrt[3]{7}\right)^{3} =7 ^a?$

Which of the following is equivalent to $5^{-\frac{1}{4}}$?

×
user
The text passage contains multiple mathematical questions involving rational exponents and their simplification or evaluation. No answers are provided for these questions.

TYPE: MULTIPLE_QUESTIONS