High School Rational exponents and radicals problems, solved and explained

Recent questions in Rational exponents and radicals

Rational exponents and radicals

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asked 2021-06-22

Simplify: \(\displaystyle{x}^{{4}}×{x}^{{2}}\)

Rational exponents and radicals

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asked 2021-06-02

\(\sqrt{(x+8)}+\sqrt{(x+15)}-\sqrt{(9x+40)}\)

Rational exponents and radicals

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asked 2021-03-07

To calculate the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{x}^{{{12}}}\right\rbrace}\) to rational exponent form and simplify.

Rational exponents and radicals

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asked 2021-03-07

To calculate:
To convert the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{x}^{{{6}}}\ {y}^{{{9}}}\right\rbrace}\) to rational exponent form and simlify.

Rational exponents and radicals

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asked 2021-03-05

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
\(\displaystyle{\frac{{\sqrt{{{3}}}{\left\lbrace{8}{x}^{{{2}}}\right\rbrace}}}{{\sqrt{{{x}}}}}}\)

Rational exponents and radicals

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asked 2021-03-01

Simplify radicals and exponents \(\sqrt[3]{(x^{3}\ y)^{2}y^{4}}\)

Rational exponents and radicals

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asked 2021-02-26

A cylindrical can, open at the top, is to hold \(470cm^{3}\) of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent pi.
Radius \(= ?\)
Height \(= ?\)

Rational exponents and radicals

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asked 2021-02-25

To determine:
The simplified value of the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{2}{a}\right\rbrace}\cdot\sqrt{{{2}{a}}}\)

Rational exponents and radicals

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asked 2021-02-25

To calculate: The expression with the help of rational exponents \(\displaystyle\sqrt{{{11}{t}}}\)

Rational exponents and radicals

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asked 2021-02-25

Now that I know how to solve radical equations, I can use models that are radical functions to determine the value of independent variable when a function value is known. We need to determine whether this statement makes sense or not.

Rational exponents and radicals

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asked 2021-02-22

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
a) \(r^{^1/_6}\ r^{^5/_6}\)
b) \(a^{^3/_5}\ a^{^3/_{10}}\)

Rational exponents and radicals

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asked 2021-02-21

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of \(f(x) = 5x^{3}\ -\ x^{2}\ +\ 5x\ -\ 1\)

Rational exponents and radicals

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asked 2021-02-21

Perform the indicated operation and express all answers with a rational denominator \(2a^{2}b\sqrt[3]{4a^{3}b}\ \cdot\ -6ab^{2}\sqrt[3]{18ab^{4}}\)

Rational exponents and radicals

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asked 2021-02-19

Reviewing for precalc and I dont understand how to completely factor expressions with rational exponents.
\(a) x^\frac{5}{2} - 9x^{\frac{1}{2}}\)
\(b) x^{-\frac{2}{3}}+2x(-\frac{1}{2})+x^{\frac{1}{2}}\)

Rational exponents and radicals

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asked 2021-02-18

Simplify the expression, answering with rational exponents and not radicals. To enter \(\displaystyle{x}^{{\frac{{m}}{{n}}}},\) type \(\displaystyle{x}^{{{\left(\frac{{m}}{{n}}\right)}}}.\)
\(\displaystyle\sqrt{{{7}}}{\left\lbrace{n}\right\rbrace}\sqrt{{{7}}}{\left\lbrace{n}\right\rbrace}=?\)

Rational exponents and radicals

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asked 2021-02-13

We need to calculate: The simplified value of the radical expression \(\sqrt[3]{\sqrt[3]{2a}}\)

Rational exponents and radicals

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asked 2021-02-12

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
\(\frac{\sqrt[3]{8x^{2}}}{\sqrt{x}}\)

Rational exponents and radicals

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asked 2021-02-11

To determine:
To calculate:
a) The indicated operation \(\displaystyle\sqrt{{{4}}}{\left\lbrace{c}{d}\right\rbrace}\cdot\sqrt{{{5}}}{\left\lbrace{c}^{{{2}}}\right\rbrace}\)
b) The indicated operation \(\displaystyle\sqrt{{{4}}}{\left\lbrace{y}\sqrt{{{3}}}{\left\lbrace{y}\right\rbrace}\right\rbrace}\)
c) The indicated operation \(\displaystyle\sqrt{{{5}}}{\left\lbrace{x}\right\rbrace}+\sqrt{{{5}}}{\left\lbrace{y}\right\rbrace}+\sqrt{{{4}}}{\left\lbrace{x}\right\rbrace}\)

Rational exponents and radicals

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asked 2021-02-11

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{5}{x}^{{{2}}}+{6}\)

Rational exponents and radicals

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asked 2021-02-10

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Simplify: \(\displaystyle{x}^{{4}}×{x}^{{2}}\)

\(\sqrt{(x+8)}+\sqrt{(x+15)}-\sqrt{(9x+40)}\)

To calculate the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{x}^{{{12}}}\right\rbrace}\) to rational exponent form and simplify.

To calculate:
To convert the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{x}^{{{6}}}\ {y}^{{{9}}}\right\rbrace}\) to rational exponent form and simlify.

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
\(\displaystyle{\frac{{\sqrt{{{3}}}{\left\lbrace{8}{x}^{{{2}}}\right\rbrace}}}{{\sqrt{{{x}}}}}}\)

Simplify radicals and exponents \(\sqrt[3]{(x^{3}\ y)^{2}y^{4}}\)

A cylindrical can, open at the top, is to hold \(470cm^{3}\) of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent pi.
Radius \(= ?\)
Height \(= ?\)

To determine:
The simplified value of the radical expression \(\displaystyle\sqrt{{{3}}}{\left\lbrace{2}{a}\right\rbrace}\cdot\sqrt{{{2}{a}}}\)

To calculate: The expression with the help of rational exponents \(\displaystyle\sqrt{{{11}{t}}}\)

Now that I know how to solve radical equations, I can use models that are radical functions to determine the value of independent variable when a function value is known. We need to determine whether this statement makes sense or not.

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
a) \(r^{^1/_6}\ r^{^5/_6}\)
b) \(a^{^3/_5}\ a^{^3/_{10}}\)

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of \(f(x) = 5x^{3}\ -\ x^{2}\ +\ 5x\ -\ 1\)

Perform the indicated operation and express all answers with a rational denominator \(2a^{2}b\sqrt[3]{4a^{3}b}\ \cdot\ -6ab^{2}\sqrt[3]{18ab^{4}}\)

Reviewing for precalc and I dont understand how to completely factor expressions with rational exponents.
\(a) x^\frac{5}{2} - 9x^{\frac{1}{2}}\)
\(b) x^{-\frac{2}{3}}+2x(-\frac{1}{2})+x^{\frac{1}{2}}\)

Simplify the expression, answering with rational exponents and not radicals. To enter \(\displaystyle{x}^{{\frac{{m}}{{n}}}},\) type \(\displaystyle{x}^{{{\left(\frac{{m}}{{n}}\right)}}}.\)
\(\displaystyle\sqrt{{{7}}}{\left\lbrace{n}\right\rbrace}\sqrt{{{7}}}{\left\lbrace{n}\right\rbrace}=?\)

We need to calculate: The simplified value of the radical expression \(\sqrt[3]{\sqrt[3]{2a}}\)

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
\(\frac{\sqrt[3]{8x^{2}}}{\sqrt{x}}\)

Graph each polynomial function. \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{5}{x}^{{{2}}}+{6}\)

To calculate : The value of addition of the rational expression \(\frac{2}{9c}\ +\ \frac{7}{15c^{3}}\)

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Rational exponents and radicals solution