Power Law of Exponent

Q. $(60\times 0.06\times 6)-(0.0006\times 600\times 0.6)$ is equal to:

1. 21.384

2. 213.84

3. 2.1834

4. 20.484

Q.

When $2^{10}$ and ${10}^2$ are compared, ${10}^2$ is greater.

1. True

2. False

Q.

$(x^m{)}^n$ is equal to:

1. $x^{(m+n)}$

2. $x^{mn}$

3. $\frac{m}{x^n}$

4. $x^{(m-n)}$

Q.

${\left(\right(2{)}^2)}^2\times (3^3÷4^2)÷3^2$ is equal to _____.

1. 3

2. 1

3. $\frac{12}{3}$
4. 27

Q.

What is the value of ${\left(\right(2{)}^{-1})}^{-2}$ ?

1. 4

2. 5

3. 2

4. 3

Q. $(2^3{)}^{-3}\text{is equal to}$.

1. $2^{-9}$
2. $2^{-1}$
3. $2^{-6}$
4. $2^0$

Q.

Evaluate $(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

1. $\frac{-1}{9}$

2. $\frac{-1}{27}$

3. $\frac{1}{9}$

4. $\frac{1}{27}$

Q. If
$3^{1+x}\times 5^y={45}^2$
then
$x=$
$y=$

1. 3
2. 2
3. 1
4. \N

Q.

When $2^{10}$ and ${10}^2$ are compared, ${10}^2$ is greater. State true or False.

1. True

2. False

Q.

Let $x$ and $y$ be natural numbers. If $x$divides $y$, then $x^3$ divides $y^3$. State whether the statement is true or false.

1. True
2. False

Q. Match the powers of '3' with their corresponding reduced powers.

1. $3^6$
2. $3^{-6}$
3. $3^9$

Q.

Evaluate $(3x^2{)}^{-3}\times (x^9{)}^{\frac{2}{3}}$

1. $\frac{-1}{9}$

2. $\frac{1}{9}$

3. $\frac{-1}{27}$

4. $\frac{1}{27}$

Q.

Which of the following is not equal to $y^6$?

1. ${\left(y^{\frac{1}{3}}\right)}^{12}$

2. ${\left(y^{\frac{2}{3}}\right)}^9$

3. ${\left(\sqrt{y^6}\right)}^2$

4. $\sqrt[3]{3y^{18}}$

Q. Simplification of ${18}^2$ to its prime factors is .

1. $2^2\times 3^4$
2. $2\times 3^2$
3. $2\times 3$

Q.

${\left(\right(2{)}^2)}^2\times (3^3÷4^2)÷3^2$ is equal to

1. $\frac{12}{3}$

2. 3

3. 1

4. 27

Q.

Find the value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}.$

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

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

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

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

Q. $4^5\times 4^4\text{is equal to}$.

1. $4^9$
2. $4^8$
3. $4^1$
4. $4^7$

Q.

Find $2.56÷0.0256$

Q.

MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION

Find the product or quotient. Write your answer in scientific notation.

$(7.2\times {10}^{-1})\times (4\times {10}^{-7})$

Q.

Which one is greater $3^{5}or{5}^3$ :

1. $3^5$

2. $5^3$

3. equal

Q. Match the powers of '3' with their corresponding reduced powers.

1. $3^6$
2. $3^9$
3. $3^{-6}$

Q. $x^6÷x^4$=

1. $x^2$
2. $x^4$
3. $x^6$

Q.

Express $8^{-2}$ as a exponent with base 2 :

1. $2^{-6}$

2. $2^{-8}$

3. $2^{-4}$

4. $8^{-4}$

Q.

${\left({12}^5\right)}^6$ = ${12}^{56}$

1. True

2. False

Q. $3^{2^3}$=

1. $3^6$
2. $3^8$
3. $3^5$

Q. Simplify:
$0\times {10}^2$

Q. Mark the greatest number of all:
$3.1\times {10}^3$, $3\times {10}^2$ and $1.1\times {10}^5$

1. $3.1\times {10}^3$
2. $3\times {10}^2$
3. $1.1\times {10}^5$
4. Can't say anything

Q. Which of the following numbers is greatest of all?
$2^3\times {10}^7,3^2\times {10}^7$ and $4^2\times {10}^7$

1. $2^3\times {10}^7$
2. $3^2\times {10}^7$
3. $4^2\times {10}^7$
4. Can't say anything

Q. Identify the greater number in the following numbers:
${100}^2$ or $2^{100}$

Q. If $a^x=\sqrt{b},b^y=\sqrt[3]{3c}$ and $c^z=\sqrt{a}$ then the value of $xyz$ is

1. $\frac{1}{2}$
2. $\frac{1}{12}$
3. $\frac{1}{3}$
4. $\frac{1}{6}$