Powers with Positive and Negative Exponents

Q.

Simplify and express each of the following in exponential form: $\frac{(2^3\times 3^4\times 4)}{(3\times 32)}$.

Q.

What is the value of ${10}^{-6}?$

Q.

In representation of 2 to the power of n, what is n called?

1. Base

2. Exponent

3. Constant

4. Inverse

Q.

If $\frac{\left(a^{n+1}+b^{n+1}\right)}{\left(a^n+b^n\right)}$ is the H.M of $a$ and $b$ then $n=\left(a,b\in R^{+},a\ne b\right)$.

1. $0$

2. $-1$

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

4. $-2$

Q. The value of $5^3$ is

1. 125
2. 145
3. 155
4. 105

Q.

$2^{-2}=0.25$ State whether true or false.

1. False

2. True

Q. Find the value of $7^{-3}$.

1. $\frac{1}{49}$
2. $\frac{1}{494}$
3. $\frac{1}{343}$
4. $\frac{1}{7}$

Q. Express $(a^3{b}^{-5}{)}^{-2}$ in positive exponent form.

1. Positive

2. Negative

3. Zero

4. Fractional number

Q.

$3^{-2}$ is equal to

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

2. $3^2$
   
   

3. $-3^2$
   

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

Q. Which of the following powers do not have negative exponents?

1. $-2^{-6}$
2. $8^{-4}$
3. ${-1}^4$
4. $5^2$

Q. $(-x{)}^{-y}$ is equal to

1. $\frac{1}{(-x{)}^y}$
2. $x^y$
3. $\frac{1}{(x{)}^y}$
4. $x^{-y}$

Q. The value of $(2^{-1}{)}^{-3}$ is ____.

1. -8
2. 8
3. 1
4. 0

Q.

$x^m÷y^m=(x÷y{)}^m,$ where $x$ and $y$ are non-zero rational numbers and $m$ is a positive integer.

Q. Find the value of ${0.2}^2\times 5^2$.

Q. What is the positive exponent of $x^{-7}$?

1. $\frac{1}{x^{-7}}$
2. $\frac{1}{x^7}$
   
3. $\frac{1}{x^6}$
4. $x^7$

Q.

Arrange the following in ascending order.

$\frac{4}{5},\frac{7}{11},\frac{9}{16},\frac{6}{8},\frac{5}{12}$

Q.

$(-1{)}^{-3}$ is :

1. -1

2. 2

3. 1

4. 0

Q.

Simplify :$\left(\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}}\right)÷\frac{1}{5^{(-2)}}$

1. (25/9)²

2. (3/5)²

3. (9/25)²

4. (5/3)²

Q.

Simplify:$(\frac{(\frac{1}{5}{)}^{-3}-(\frac{1}{3}{)}^{-4}}{(\frac{1}{4}{)}^{-3}})$

1. $\frac{12}{13}$

2. $\frac{13}{12}$

3. $\frac{16}{11}$

4. $\frac{11}{16}$

Q. If 3 is multiplied by itself ten times, it can be written as ____

1. $3^{10}$
2. $3\times 10$
3. ${10}^3$
4. 3+10

Q. Which of the following has the greatest value?

1. $(6^2\times 6{)}^4$
2. $({36}^2\times 6^3{)}^2$
3. $(216{)}^4$
4. $(36{)}^5$
5. $(6^4{)}^4$

Q. How do you evaluate and simplify ${27}^{\frac{2}{3}}$?

Q. $\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}$ can be written as

1. $\frac{1}{5^4}$
2. $\frac{1}{5^{-4}}$
3. $5^4$
4. $5^{-4}$

Q.

Simplify :$\left\{\frac{1}{6^{(-2)}}-\frac{1}{3^{(-2)}}\right\}÷\frac{1}{5^{(-2)}}$

1. (3/5)²

2. (9/25)²

3. (25/9)²

4. (5/3)²

Q.

Identify the exponential form of $3^2\times 3^4\times 3^8$.

1. $3^{12}$
2. $3^{10}$
3. $3^6$
4. $3^{14}$

Q. Which of the following equations are correctly written?

1. $\frac{a^m}{b^m}$ = ${\left(\frac{a}{b}\right)}^m$
2. $\frac{a^m}{b^n}$ = ${\left(\frac{a}{b}\right)}^{m-n}$
3. $a^m\times a^n$ = ${\left(a\right)}^{mn}$
4. $\frac{a^m}{a^n}$ = ${\left(a\right)}^{m-n}$

Q.

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

$a^3÷b^3$

Q. Express the following in exponential form: $\frac{-5}{7}\times \frac{-5}{7}\times \frac{-5}{7}\times \frac{-5}{7}$

Q.

$a\times a\times a.....(15times)=a^{16}$

1. True
2. False

Q.

Simplify the following :

${\left(\frac{2}{3}\right)}^4\times 3^2\times {\left(\frac{-1}{2}\right)}^5$