Indices in Rational Form

Q. ${36}^{\frac{1}{2}}$ = _______

1. 1
2. 0
3. 18
4. 6

Q. If $a^2+\frac{1}{a^2}=11$ find $a-\frac{1}{a}$

Q. ${16}^{\frac{3}{4}}$ = _______

1. 2
2. 6
3. 8
4. 4

Q. If $7^3=343$ then $\sqrt[3]{3343}=?$

1. $9$
2. $7^3$
3. $7$
4. $1/7$

Q.

\({a}^{(\frac{m}{n})}\) can be written as:

Q. $4^{\frac{3}{2}}$ = ______

1. 1
2. 6
3. 8
4. 2

Q. Write the surds in radical form:
${142}^{\frac{1}{2}}$

Q. $4^{\frac{3}{2}}$ =.

1. 8
2. 16
3. 4
4. 64

Q. Evaluate :
(a) $\sqrt[8]{8\frac{6561}{65536}}$ (b) ${\left(15625\right)}^{\frac{1}{6}}$.

Q. $\sqrt[3]{3\sqrt[3]{3a^3}}$ is equal to

1. $a$
2. $1$
3. $a^{\frac{1}{3}}$
4. $a^3$

Q. Evaluate the following
$\sqrt[3]{3-\frac{10648}{12167}}$

Q. The value of $\sqrt[4]{4(64{)}^{-2}}$ is :

1. $\frac{1}{8}$
2. 8
3. $\frac{1}{2}$
4. $\frac{1}{64}$

Q. Evaluate: $3^2$

Q. $\sqrt[3]{3\left[\frac{(-1728)}{2744}\right]}$

1. $\frac{-6}{11}$
2. $\frac{-6}{7}$
3. $\frac{-12}{14}$
4. $\frac{-3}{4}$

Q. $\sqrt{\frac{36a^4{b}^6}{144a^6{b}^4}}$ = ?

1. $\left|\frac{1}{2}\frac{b}{a}\right|$
2. $2\left|\frac{b}{a}\right|$
3. $\frac{1}{2}\left|\frac{b}{a}\right|$
4. $\frac{3}{2}\left|\frac{b}{a}\right|$

Q. Evaluate ${32}^{3/5}.$

Q. Which of the following is equal to $a^{\frac{2}{3}}$, for all values of a?

1. $\sqrt{a^{\frac{1}{3}}}$
2. $\sqrt{a^3}$
3. $\sqrt[3]{3a^{\frac{1}{2}}}$
4. $\sqrt[3]{3a^2}$

Q. Evaluate ${\left(\frac{x^a}{x^{-b}}\right)}^{a-b}.{\left(\frac{x^b}{x^{-c}}\right)}^{b-c}.{\left(\frac{x^c}{x^{-a}}\right)}^{c-a}$

1. 8
2. 4
3. 2
4. 1

Q. $({27}^{-2}{)}^{1/3}\times \sqrt{4^3}=$___

1. 7/9
2. 8/9
3. 9/9
4. 10/9

Q.

How do you evaluate ${(-1)}^{\frac{2}{3}}$?