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Basic Arithmetic

Please Excuse My Dear Aunt Sally (PEMDAS), she has the hardest time remembering how to make sense of these arithmetic rules...

Rational Exponents

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

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

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

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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