1.
Item 1. Write as a single power. \(\frac{7^{-3}}{7^{-5}}\) = ?
Solution: Subtract the exponents when dividing powers with the same base. \(\frac{7^{-3}}{7^{-5}}=7^{-3-(-5)}=7^2\). Answer: B
2.
Item 5. Evaluate. Leave your answer in exact form, no decimals. \((16^{0.5})^{0.5}\)
Solution: \(16^{0.5}=\sqrt{16}=4\). Then \(4^{0.5}=\sqrt{4}=2\). Answer: B
3.
Item 3. Simplify. \(\frac{15a^3b}{-14} \times \frac{-28ab^{-1}}{9a^5b^2}\)
Solution: Multiply and simplify. The negatives cancel, \(15 \times 28 \div (14 \times 9)=10/3\). For variables, \(a^{3+1-5}=a^{-1}\) and \(b^{1-1-2}=b^{-2}\). So the result is \(\frac{10}{3ab^2}\). Answer: A
4.
Item 2. Simplify, if possible. \((-48k^{12}m^{5}n^{-8}) \div (6k^{-3}m^{-5}n^{-7})\)
Solution: Divide coefficients and subtract exponents. \(-48 \div 6=-8\), \(k^{12-(-3)}=k^{15}\), \(m^{5-(-5)}=m^{10}\), \(n^{-8-(-7)}=n^{-1}\). Answer: D
5.
Item 6. Which expression is the exponential form of \(\sqrt[11]{(-24)^{17}}\)?
Solution: \(\sqrt[11]{(-24)^{17}}=\left((-24)^{17}\right)^{1/11}=(-24)^{17/11}\). Answer: B
6.
Item 4. Identify the base in the following expression. \(-51(cd)^6\)
Solution: The base is the bracketed expression immediately before the exponent. In \(-51(cd)^6\), the base is \(cd\). Answer: C
7.
Item 8. Reorder from Least to Greatest. \(5, \sqrt{4}, \sqrt{36}, 7, \sqrt{9}\)
Solution: Evaluate each expression: \(\sqrt{4}=2\), \(\sqrt{9}=3\), \(5=5\), \(\sqrt{36}=6\), \(7=7\). From least to greatest: \(\sqrt{4}, \sqrt{9}, 5, \sqrt{36}, 7\). Answer: B
8.
Item 7. Evaluate. \(\sqrt[3]{216}\)
Solution: \(\sqrt[3]{216}=\sqrt[3]{6 \times 6 \times 6}=6\). Answer: B
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