Write each radical expression using exponents and each exponential expression using radicals. Radical expression Exponential expression sqrt[3]{y^{4}}

Write each radical expression using exponents and each exponential expression using radicals. Radical expression Exponential expression sqrt[3]{y^{4}}

Question
Exponents and radicals
asked 2021-01-22
Write each radical expression using exponents and each exponential expression using radicals. Radical expression Exponential expression \(\sqrt[3]{y^{4}}\)

Answers (1)

2021-01-23
For any rational exponent \(m/_n\) in lowest terms, where m and n are integers and \(n > 0\), we define \(a\ m/_n=(\sqrt[n]{a})^{m}\) or equivalently \(a^{m/_n}=\sqrt[n]{{a}^{m}}\). If n is even, then we require that \(a >= 0\). Given: \(\sqrt[3]{y^{4}}\) Calculation: Consider, \(\sqrt[3]{y^{4}}\) From the above definition \(a^{m/_n}\) the exponential notation of \(\sqrt[3]{y^{4}}\) is written as, \(\sqrt[3]{y^{4}} = (y^{4})^{\frac{1}{3}}\)
\(= y^{\frac{4}{3}}\) Therefore, using exponential notation, we can write \(\sqrt[3]{y^{4}}\ \text{as}\ y^{\frac{4}{3}}\)
0

Relevant Questions

asked 2020-10-21
Write each radical expression using exponents and each exponential expression using radicals.
\(\frac{Radical\ expression\ Exponential\ expression}{\sqrt[5]{5^{3}}}\)
asked 2021-01-31
Radical and Exponents Simplify the expression \(\frac{(ab^2 c^-3}{2a^3 b^-4)}^{-2}\)
asked 2020-11-22
Radical and Exponents Simplify the expression \(\frac{8r^(1/2)s^-3}{2r^-2 x^4}\)
asked 2021-01-17
Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. \(\displaystyle{\sqrt[{{5}}]{{{x}^{{20}}{y}^{{-{{4}}}}}}}\)
asked 2021-03-04
Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. \(a*(1/81)^(-1/4)b*x^(-2)y^(-4)c*(2x)^(-2)(16x^2y)^(1/2)\)
asked 2020-11-07
Describe the process used to solve an equation with two radical expressions. How is this process different from solving an equation with only one radical expression?
asked 2021-01-08
Radicals and Exponents Evaluate each expression:
a) \(\displaystyle{\frac{{\sqrt{{{132}}}}}{{\sqrt{{{3}}}}}}\)
b) \(\displaystyle\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}\sqrt{{{3}}}{\left\lbrace{32}\right\rbrace}\)
c) \(\displaystyle\sqrt{{{4}}}{\left\lbrace{\frac{{{1}}}{{{4}}}}\right\rbrace}\sqrt{{{4}}}{\left\lbrace{\frac{{{1}}}{{{64}}}}\right\rbrace}\)
asked 2020-12-01
Radical simplify the expression, and eliminate any negative exponents(s). Assume that all letters denote positive numbers.
a) \(\displaystyle\sqrt{{{6}}}{\left\lbrace{y}^{{{5}}}\right\rbrace}\sqrt{{{3}}}{\left\lbrace{y}^{{{2}}}\right\rbrace}\)
b) \(\displaystyle{\left({5}\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}\right)}{\left({2}\sqrt{{{4}}}{\left\lbrace{x}\right\rbrace}\right)}\)
asked 2021-03-09
Simplify: \(\displaystyle{\left({7}^{{5}}\right)}{\left({4}^{{5}}\right)}\). Write your answer using an exponent.
Explain in words how to simplify: \(\displaystyle{\left({153}^{{2}}\right)}^{{7}}.\)
Is the statement \(\displaystyle{\left({10}^{{5}}\right)}{\left({4}^{{5}}\right)}={14}^{{5}}\) true?
asked 2021-02-09
Use rational exponents to write a single radical expression \(\left(\sqrt[3]{x^{2}y^{5}}\right)^{12}\)
...