Exponent Properties Mid Chapter Review
Chapter
Chapter 4
Section
Exponent Properties Mid Chapter Review
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Solutions 50 Videos

Write as a single power. Express your answers with positive exponents.

\displaystyle 5 (5^4)

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Q1a

Write as a single power. Express your answers with positive exponents.

\displaystyle \frac{(-8)^4}{(-8)^5}

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Q1b

Write as a single power. Express your answers with positive exponents.

\displaystyle (9^3)^6

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Q1c

Write as a single power. Express your answers with positive exponents.

\displaystyle \frac{3\cdot 3^6}{3^5}

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Q1d

Write as a single power. Express your answers with positive exponents.

\displaystyle (\frac{1}{10})^6(\frac{1}{10})^{-4}

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Q1e

Write as a single power. Express your answers with positive exponents.

\displaystyle (\frac{7^2}{7^4})^{-4}

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Q1f

Evaluate. Express answers in rational form.

\displaystyle 4^{-2} - 8^{-1}

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Q2a

Evaluate. Express answers in rational form.

\displaystyle (4 + 8)^0 -5^{-2}

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Q2b

Evaluate. Express answers in rational form.

\displaystyle 25^{-1} + 3(5^{-1})^2

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Q2c

Evaluate. Express answers in rational form.

\displaystyle (- \frac{1}{2})^3 + 4^{-3}

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Q2d

Evaluate. Express answers in rational form.

\displaystyle (\frac{4}{7})^2

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Q3a

Evaluate. Express answers in rational form.

\displaystyle (-\frac{2}{5})^3

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Q3b

Evaluate. Express answers in rational form.

\displaystyle (\frac{-2}{3})^{-3}

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Q3c

Evaluate. Express answers in rational form.

\displaystyle \frac{(-3)^{-2}}{(-3)^{-5}}

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Q3d

What restrictions are there on the value of x in x^{-\frac{1}{2}}? Are these restrictions different for x^2? Explain.

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Q4

Evaluate. Express answers in rational form.

\displaystyle (\frac{49}{81})^{\frac{1}{2}}

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Q5a

Evaluate. Express answers in rational form.

\displaystyle \sqrt{\frac{100}{121}}

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Q5b

Evaluate. Express answers in rational form.

\displaystyle (\frac{16}{9})^{-0.5}

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Q5c

Evaluate. Express answers in rational form.

\displaystyle ((-125)^{\frac{1}{3}})^{-3}

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Q5d

Evaluate. Express answers in rational form.

\displaystyle \sqrt[4]{(-9)^{-2}}

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Q5e

Evaluate. Express answers in rational form.

\displaystyle \frac{-\sqrt[3]{512}}{\sqrt[5]{-1024}}

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Q5f

Convert 100^{\frac{1}{2}} into radical form and evaluate the expression.

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Q6a

Convert 16^{\frac{1}{4}} into radical form and evaluate the expression.

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Q6b

Convert \sqrt{121} into exponential form and evaluate the expression.

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Q6c

Convert \displaystyle (-27)^{\frac{5}{3}} into radical form and evaluate the expression.

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Q6d

Convert \displaystyle 49^{2.5} into radical form and evaluate the expression.

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Q6e

Convert \displaystyle \sqrt[10]{1024} into exponential form and evaluate the expression.

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Q6f

Evaluate. Express answers to three decimals.

\displaystyle -456^{\frac{4}{7}}

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Q7a

Evaluate. Express answers to three decimals.

\displaystyle 98^{0.75}

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Q7b

Evaluate. Express answers to three decimals.

\displaystyle (\frac{5}{8})^{\frac{5}{8}}

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Q7c

Evaluate. Express answers to three decimals.

\displaystyle (\sqrt[5]{-1000})^3

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Q7d

Evaluate -8^{\frac{4}{3}} and (-8)^{\frac{4}{3}}. Explain the difference between the two.

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Q8

Simplify and express your answers with positive exponents.

\displaystyle \frac{(x^{-3})x^5}{x^7}

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Q9a

Simplify and express your answers with positive exponents.

\displaystyle \frac{(n^{-4})n^{-6}}{(n^{-2})^7}

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Q9b

Simplify and express your answers with positive exponents.

\displaystyle (\frac{(y^2)^6}{y^9})^{-2}

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Q9c

Simplify and express your answers with positive exponents.

\displaystyle \frac{(-2x^5)^3}{8x^{10}}

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Q9d

Simplify and express your answers with positive exponents.

\displaystyle (3a^2)^{-3}(9a^{-1})^2

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Q9e

Simplify and express your answers with positive exponents.

\displaystyle \frac{(4r^{-6})(-2r^2)^5}{(-2r)^4}

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Q9f

Simplify and express your answers with positive exponents.

\displaystyle \frac{x^{0.5}y^{1.8}}{x^{0.3}y^{2.5}}

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Q10a

Simplify and express your answers with positive exponents.

\displaystyle \frac{(mn^3)^{-\frac{1}{2}}}{m^{\frac{1}{2}}n^{- \frac{5}{2}}}

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Q10b

Simplify and express your answers with positive exponents.

\displaystyle \frac{\sqrt{x^2y^4}}{(x^{-2}y^3)^{-1}}

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Q10c

Simplify and express your answers with positive exponents.

\displaystyle (\frac{2abc^3}{(2a^2b^3c)^2})^{-2}

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Q10d

Simplify and express your answers with positive exponents.

\displaystyle \frac{\sqrt[4]{81p^8}}{\sqrt{9p^4}}

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Q10e

Simplify and express your answers with positive exponents.

\displaystyle \frac{\sqrt[6]{(8x^6)^2}}{\sqrt[4]{625x^8}}

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Q10f

Evaluate each expression for a = 2 and b = 3. Express values in rational form.

\displaystyle (\frac{b^3}{a^{\frac{5}{2}}})^2 (\frac{2a^4}{b^5})

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Q11a

Evaluate each expression for a = 2 and b = 3. Express values in rational form.

\displaystyle \sqrt{\frac{9b^3(ab)^2}{(a^2b^3)^3}}

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Q11b

Simplify.

\displaystyle (a^{10 + 2p})(a^{-p-8})

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Q12a

Simplify.

\displaystyle (2x^2)^{3 -2m}(\frac{1}{x})^{2m}

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Q12b

Simplify.

\displaystyle [c^{2n -3m}](c^3)^m \div (c^2)^n

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Q12c

Simplify.

\displaystyle (x^{4n -m})(\frac{1}{x^3})^{m + n}

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Q12d