Gr 11 Math Ch 1: Rational Exponents and Surds

What is the value of $r$ if $r^3 = 27$?

$3$

What is the value of $a^{rac{2}{3}}$ if $a = 8$?

$\sqrt[3]{8^2}$

What is the value of $\sqrt[4]{81}$?

$3$

What is the value of $(\sqrt{16})^2$?

$16$ Signup and view all the answers

What is the value of $\sqrt{12} imes \sqrt{3}$?

$2\sqrt{3}$ Signup and view all the answers

What is the value of $rac{\sqrt{50}}{\sqrt{2}}$?

$rac{5}{2}$ Signup and view all the answers

What is the value of $\sqrt[3]{27} imes \sqrt[3]{8}$?

$\sqrt[3]{216}$ Signup and view all the answers

What is the value of $2^{rac{3}{2}}$?

$\sqrt{2^3}$ Signup and view all the answers

What is the definition of $r$ in terms of $a$ when $r^n = a$?

$r = \sqrt[n]{a}$ Signup and view all the answers

What is the value of $a^{rac{m}{n}}$ when $a > 0$, $m, n \in \mathbb{Z}$, and $n eq 0$?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the definition of a surd?

A radical resulting in an irrational number Signup and view all the answers

What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

$\sqrt[n]{ab}$ Signup and view all the answers

What is the purpose of rationalizing the denominator?

To eliminate the surd from the denominator Signup and view all the answers

What is the result of raising $\sqrt[n]{a}$ to the power of $m$?

$a^{rac{m}{n}}$ Signup and view all the answers

What is the value of $a^{-rac{1}{n}}$?

$rac{1}{\sqrt[n]{a}}$ Signup and view all the answers

What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?

$\sqrt[n]{rac{a}{b}}$ Signup and view all the answers

If $a > 0$ and $m, n \in \mathbb{Z}$, then what is the value of $a^{rac{m}{n}}$ in terms of radicals?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the value of $\sqrt[3]{a^2} imes \sqrt[3]{a^4}$?

$a^{rac{6}{3}}$ Signup and view all the answers

What is the value of $rac{\sqrt{a}}{\sqrt{b}}$?

$\sqrt{rac{a}{b}}$ Signup and view all the answers

What is the value of $\sqrt{a} imes \sqrt[3]{a^2}$?

$a^{rac{3}{2}}$ Signup and view all the answers

What is the purpose of rationalizing the denominator of a fraction?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of $\left(\sqrt{a} ight)^3$?

$a^3$ Signup and view all the answers

What is the value of $\sqrt[4]{a^3}$?

$a^{3/4}$ Signup and view all the answers

What is the value of $\sqrt{a} imes \sqrt{b}$?

$\sqrt{a imes b}$ Signup and view all the answers

What is the value of $a^{rac{3}{2}}$ when $a = 16$?

8 Signup and view all the answers

What is the value of $\sqrt[4]{x^2}$ when $x = 9$?

3 Signup and view all the answers

What is the value of $rac{\sqrt{50}}{\sqrt{10}}$?

$\sqrt{5}$ Signup and view all the answers

What is the value of $a^{rac{2}{3}}$ when $a = 27$?

9 Signup and view all the answers

What is the value of $\sqrt[3]{x^2}$ when $x = 8$?

2 Signup and view all the answers

What is the value of $rac{\sqrt[3]{a^2}}{\sqrt[3]{a}}$ when $a = 27$?

3 Signup and view all the answers

What is the value of $a^{rac{3}{4}}$ when $a = 16$?

8 Signup and view all the answers

What is the value of $\sqrt{x^2}$ when $x = 4$?

4 Signup and view all the answers

What is the value of $a^{\frac{2}{3}}$ when $a = 27$?

$3\sqrt{3}$ Signup and view all the answers

What is the purpose of rationalizing the denominator of a fraction?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of $\sqrt[3]{a^2} \times \sqrt[3]{a^4}$ when $a > 0$?

$a^{2}$ Signup and view all the answers

What is the value of $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ when $a, b > 0$ and $n \in \mathbb{Z}$?

$\sqrt[n]{\frac{a}{b}}$ Signup and view all the answers

What is the definition of a surd?

A radical resulting in an irrational number Signup and view all the answers

Gr 11 Math Ch 1: Rational Exponents and Surds

Questions and Answers

What is the value of $r$ if $r^3 = 27$?

What is the value of $a^{rac{2}{3}}$ if $a = 8$?

What is the value of $\sqrt[4]{81}$?

What is the value of $(\sqrt{16})^2$?

What is the value of $\sqrt{12} imes \sqrt{3}$?

What is the value of $rac{\sqrt{50}}{\sqrt{2}}$?

What is the value of $\sqrt[3]{27} imes \sqrt[3]{8}$?

What is the value of $2^{rac{3}{2}}$?

What is the definition of $r$ in terms of $a$ when $r^n = a$?

What is the value of $a^{rac{m}{n}}$ when $a > 0$, $m, n \in \mathbb{Z}$, and $n eq 0$?

What is the definition of a surd?

What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

What is the purpose of rationalizing the denominator?

What is the result of raising $\sqrt[n]{a}$ to the power of $m$?

What is the value of $a^{-rac{1}{n}}$?

What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?

If $a > 0$ and $m, n \in \mathbb{Z}$, then what is the value of $a^{rac{m}{n}}$ in terms of radicals?

What is the value of $\sqrt[3]{a^2} imes \sqrt[3]{a^4}$?

What is the value of $rac{\sqrt{a}}{\sqrt{b}}$?

What is the value of $\sqrt{a} imes \sqrt[3]{a^2}$?

What is the purpose of rationalizing the denominator of a fraction?

What is the value of $\left(\sqrt{a} ight)^3$?

What is the value of $\sqrt[4]{a^3}$?

What is the value of $\sqrt{a} imes \sqrt{b}$?

What is the value of $a^{rac{3}{2}}$ when $a = 16$?

What is the value of $\sqrt[4]{x^2}$ when $x = 9$?

What is the value of $rac{\sqrt{50}}{\sqrt{10}}$?

What is the value of $a^{rac{2}{3}}$ when $a = 27$?

What is the value of $\sqrt[3]{x^2}$ when $x = 8$?

What is the value of $rac{\sqrt[3]{a^2}}{\sqrt[3]{a}}$ when $a = 27$?

What is the value of $a^{rac{3}{4}}$ when $a = 16$?

What is the value of $\sqrt{x^2}$ when $x = 4$?

What is the value of $a^{\frac{2}{3}}$ when $a = 27$?

What is the purpose of rationalizing the denominator of a fraction?

What is the value of $\sqrt[3]{a^2} \times \sqrt[3]{a^4}$ when $a > 0$?

What is the value of $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ when $a, b > 0$ and $n \in \mathbb{Z}$?

What is the definition of a surd?

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