Write as a single power. Express your answers with positive exponents.
\displaystyle
5 (5^4)
Write as a single power. Express your answers with positive exponents.
\displaystyle
\frac{(-8)^4}{(-8)^5}
Write as a single power. Express your answers with positive exponents.
\displaystyle
(9^3)^6
Write as a single power. Express your answers with positive exponents.
\displaystyle
\frac{3\cdot 3^6}{3^5}
Write as a single power. Express your answers with positive exponents.
\displaystyle
(\frac{1}{10})^6(\frac{1}{10})^{-4}
Write as a single power. Express your answers with positive exponents.
\displaystyle
(\frac{7^2}{7^4})^{-4}
Evaluate. Express answers in rational form.
\displaystyle
4^{-2} - 8^{-1}
Evaluate. Express answers in rational form.
\displaystyle
(4 + 8)^0 -5^{-2}
Evaluate. Express answers in rational form.
\displaystyle
25^{-1} + 3(5^{-1})^2
Evaluate. Express answers in rational form.
\displaystyle
(- \frac{1}{2})^3 + 4^{-3}
Evaluate. Express answers in rational form.
\displaystyle
(\frac{4}{7})^2
Evaluate. Express answers in rational form.
\displaystyle
(-\frac{2}{5})^3
Evaluate. Express answers in rational form.
\displaystyle
(\frac{-2}{3})^{-3}
Evaluate. Express answers in rational form.
\displaystyle
\frac{(-3)^{-2}}{(-3)^{-5}}
What restrictions are there on the value of x
in x^{-\frac{1}{2}}
?
Are these restrictions different for x^2
? Explain.
Evaluate. Express answers in rational form.
\displaystyle
(\frac{49}{81})^{\frac{1}{2}}
Evaluate. Express answers in rational form.
\displaystyle
\sqrt{\frac{100}{121}}
Evaluate. Express answers in rational form.
\displaystyle
(\frac{16}{9})^{-0.5}
Evaluate. Express answers in rational form.
\displaystyle
((-125)^{\frac{1}{3}})^{-3}
Evaluate. Express answers in rational form.
\displaystyle
\sqrt[4]{(-9)^{-2}}
Evaluate. Express answers in rational form.
\displaystyle
\frac{-\sqrt[3]{512}}{\sqrt[5]{-1024}}
Convert 100^{\frac{1}{2}}
into radical form and evaluate the expression.
Convert 16^{\frac{1}{4}}
into radical form and evaluate the expression.
Convert \sqrt{121}
into exponential form and evaluate the expression.
Convert \displaystyle
(-27)^{\frac{5}{3}}
into radical form and evaluate the expression.
Convert \displaystyle
49^{2.5}
into radical form and evaluate the expression.
Convert \displaystyle
\sqrt[10]{1024}
into exponential form and evaluate the expression.
Evaluate. Express answers to three decimals.
\displaystyle
-456^{\frac{4}{7}}
Evaluate. Express answers to three decimals.
\displaystyle
98^{0.75}
Evaluate. Express answers to three decimals.
\displaystyle
(\frac{5}{8})^{\frac{5}{8}}
Evaluate. Express answers to three decimals.
\displaystyle
(\sqrt[5]{-1000})^3
Evaluate -8^{\frac{4}{3}}
and (-8)^{\frac{4}{3}}
. Explain the difference
between the two.
Simplify and express your answers with positive exponents.
\displaystyle
\frac{(x^{-3})x^5}{x^7}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{(n^{-4})n^{-6}}{(n^{-2})^7}
Simplify and express your answers with positive exponents.
\displaystyle
(\frac{(y^2)^6}{y^9})^{-2}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{(-2x^5)^3}{8x^{10}}
Simplify and express your answers with positive exponents.
\displaystyle
(3a^2)^{-3}(9a^{-1})^2
Simplify and express your answers with positive exponents.
\displaystyle
\frac{(4r^{-6})(-2r^2)^5}{(-2r)^4}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{x^{0.5}y^{1.8}}{x^{0.3}y^{2.5}}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{(mn^3)^{-\frac{1}{2}}}{m^{\frac{1}{2}}n^{- \frac{5}{2}}}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{\sqrt{x^2y^4}}{(x^{-2}y^3)^{-1}}
Simplify and express your answers with positive exponents.
\displaystyle
(\frac{2abc^3}{(2a^2b^3c)^2})^{-2}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{\sqrt[4]{81p^8}}{\sqrt{9p^4}}
Simplify and express your answers with positive exponents.
\displaystyle
\frac{\sqrt[6]{(8x^6)^2}}{\sqrt[4]{625x^8}}
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})
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}}
Simplify.
\displaystyle
(a^{10 + 2p})(a^{-p-8})
Simplify.
\displaystyle
(2x^2)^{3 -2m}(\frac{1}{x})^{2m}
Simplify.
\displaystyle
[c^{2n -3m}](c^3)^m \div (c^2)^n
Simplify.
\displaystyle
(x^{4n -m})(\frac{1}{x^3})^{m + n}