Rational Indices

Q.

What is the square of $\left(\frac{-2}{3}\right)$?

1. $-\frac{2}{3}$

2. $\frac{2}{3}$

3. $-\frac{4}{9}$

4. $\frac{4}{9}$

Q. The side of a square is 5 units. Area of that square would be square units.

1. 10
2. 20
3. 25
4. 30

Q.

The value of ${(7^{-1}–8^{-1})}^{-1}–{(3^{-1}–4^{-1})}^{-1}$ is

1. $44$

2. $56$

3. $68$

4. $12$

Q. Base 3 with exponent 5 can be expressed as

1. $3^5$
2. $5^3$
3. $3\times 5$

Q.

Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}$

Q.

What are exponents?

Q. Find the value of $x$ if $5^{x-7}=1$.

1. $x=5$
2. $x=1$
3. $x=6$
4. $x=7$

Q.

How do you simplify $8^{-1}$ ?

Q.

Using laws of exponents, simplify and write the answer in exponential form:

${\mathrm{a}}^3\times {\mathrm{a}}^2$

Q. What is the value of 5th root of 243?

Q. Simplify $\sqrt[3]{327P^{27}}$

1. $27P^3$
2. $3P^{27}$
3. $3P^9$
4. $3P^3$

Q. Simplify the following expression such that the result has positive exponents: $\left(25M^2{N}^{-4}{)}^{1/2}\right(M^3{N}^{1/2}{)}^2$.

1. $5M^7/N$
2. $25M^5/N$
3. $5M^5/N$
4. $5M^6/N$

Q. Simplify $(0.00032{)}^{\frac{4}{5}}.$

1. $0.0016$
2. $0.0008$
3. $0.00016$
4. $0.00008$

Q. What will $A^{1/3}\times A^{1/3}\times A^{1/3}$ be equal to?

1. $A^{1/2}$
2. $A$
3. $A^{3/2}$
4. $A^3$

Q. Guess the square root of 36.

1. 4
2. 5
3. 6
4. 8

Q. The value of $(-276{)}^0$ is .

Q. Which among the following would be equal to ${81}^{\frac{2}{3}}?$

1. Cube root of $81$
2. Square root of $81$
3. Square root of $9^4$
4. Cube root of $9^4$

Q. $\sqrt{49}$ can be written as ${49}^{\frac{1}{2}}.$

1. True
2. False

Q. Simplify the expression $(a^n{)}^{\frac{2}{n}}$.

1. $a^2$
2. $a^3$
3. $a^4$
4. $a$

Q. Find the value of $(\frac{4}{49}{)}^{\frac{3}{4}}\times (\frac{49}{4}{)}^{-\frac{1}{2}}.$

1. $\frac{4}{49}$
   
2. $\frac{49}{4}$
   
3. $(\frac{4}{49}{)}^{\frac{5}{4}}$
   
4. $(\frac{49}{4}{)}^{\frac{5}{4}}$
   

Q. Find the value of $((\frac{81}{256}{)}^{\frac{3}{4}}{)}^{-\frac{5}{3}}.$

1. $\frac{243}{1024}$
   
2. $-\frac{243}{1024}$
   
3. $-\frac{1024}{243}$
   
4. $\frac{1024}{243}$
   

Q. Cube root of $7^6$ is

1. $7^2$
2. $7^3$
3. $7^4$
4. $7^5$

Q.

Find the quotient $-24÷12$

Q. To what exponent should 16 be raised to get the desired result as 4?

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

Q.

Find the value of :

(ii) $8^3$

Q. Cube root of (7 x 7 x 7) is

Q.

Express in the exponential form.

$1+1$

Q. What is the result of $m^{\frac{1}{2}}\times m^{\frac{1}{2}}$ ?

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

Q. What will be the value of $(8{)}^{\left(3^{-1}\right)}$ ?

1. 24
2. $\frac{8}{3}$
3. 2
4. $\frac{1}{2}$