Quotient Law

Q. Explain some examples of the laws of exponents ?

Q.

For any two non-zero rational numbers $x$ and $y$, $x^5÷y^5$is equal to:

1. ${\left(x÷y\right)}^1$

2. ${\left(x÷y\right)}^0$

3. ${\left(x÷y\right)}^5$

4. ${\left(x÷y\right)}^{10}$

Q.

If $\frac{2^{(2a+1)}\times 3^{(3b+2)}}{6^2}=2^x\times 3^y$

Chose the correct option:

1. x = 2a – 1, y = 3b

2. x = 2a + 1, y = 3b + 2

3. x = 2a + 1, y = 3b

4. x = 2a + 1, y = 3b

Q. Simplify and write the answer in exponential form:
${\left(7^{50}\right)}^2$

Q.

$18a^3{b}^3{c}^2÷6abc=$

1. $2a^2{b}^{2}c$

2. $3a^2{b}^{2}c$

3. $3a^{2}bc$

4. $3abc$

Q.

For any two non-zero rational numbers $x$ and $y$, $x^4÷y^4$is equal to:

1. ${\left(x÷y\right)}^0$

2. ${\left(x÷y\right)}^1$

3. ${\left(x÷y\right)}^4$

4. ${\left(x÷y\right)}^8$

Q.

Simplify: $\frac{a^{-4}\times b^3\times c^5\times d^{-7}}{a^{-7}\times b^{-3}\times c^2\times d^{-9}}$

1. $a^3{b}^6{c}^3{d}^2$

2. $a^3{b}^5{c}^3{d}^2$

3. $a^2{b}^6{c}^3{d}^2$

4. $a^3{b}^6{c}^3{d}^4$

Q. Find the value of ${100}^{\frac{5}{2}}÷{100}^{-\frac{1}{2}}$.

1. ${10}^2$
2. ${10}^6$
3. ${10}^{-6}$
4. ${10}^4$

Q. Find the value of $x$, if $8^{x-3}={16}^{4-x}.$

1. $4$
2. $\frac{11}{3}$
3. $\frac{25}{7}$
4. $\frac{7}{2}$

Q.

Find the product of $(t+s^2)$ and $(t^2-s)$.

1. $t^3+s^2{t}^2-st-s^2$

2. $t^3+s^2{t}^2-st-s^3$

3. $t^3+s^2{t}^2-2st-s^3$

4. $t^3+t^2-st-s^3$

Q. Simplify and write the answer in exponential form:
$6^{24}÷6^9$

Q. Simplify and express each of the following in exponential form:

$(3^0+2^0)\times 5^0$ [3 MARKS]

Q.

Choose the correct word/answer and fill in the blanks:

${\left({100}^2\right)}^3$ and ${\left[{100}^3\right]}^2$ are _________ (same/different)

Q.

Evaluate ${10}^{-1}\times {10}^3\times {10}^{-5}\times {10}^3$

1. 1

2. 10

3. 100

4. $\frac{1}{10}$

Q. Find the value of $x$ if $(\frac{8}{9}{)}^5=\frac{8^5}{x}$.

1. $3^{16}$
2. $9^8$
3. $9^5$
4. $3^{10}$

Q. Simplify and write the answer in exponential form:
$6^{24}÷6^9$

Q.

Evaluate $(1^3+2^3+3^3+4^3{)}^{\frac{-3}{2}}.$

1. ${10}^{-1}$

2. ${10}^{-2}$

3. ${10}^{-4}$

4. ${10}^{-3}$

Q.

Evaluate $(25{)}^3÷5^3$

1. $128$
2. $256$
3. $125$
4. $64$

Q. Simplify $\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

1. $a^{-11}{b}^{-18}{c}^{15}$
2. $a^{11}{b}^{18}{c}^{15}$
3. $a^{-11}{b}^{18}{c}^{-15}$
4. $a^{11}{b}^{18}{c}^{-15}$

Q.

$a^m$ ÷ $a^n$ = $a^{mn}$

1. True

2. False

Q. Simplify $\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

1. $a^{11}{b}^{18}{c}^{-15}$
2. $a^{11}{b}^{18}{c}^{15}$
3. $a^{-11}{b}^{-18}{c}^{15}$
4. $a^{-11}{b}^{18}{c}^{-15}$

Q.

The value of ($4^{-7}$ ÷ $4^{-10}$ ) × $4^{-5}$ is ${16}^{-1}$.

1. True

2. False

Q. Simplify:
$2\times {10}^3$

Q.

$15y^8÷5y^6$ is $3y^2$

1. True

2. False

Q. $2^3\times 2^5$=

1. $2^8$
2. $2^4$
3. $2^{15}$

Q. The value of $\frac{(-7{)}^6}{7^6}$ is .

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

Q.

Find the value of :

(iii) $4^5$

Q.

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

1. $\frac{1}{2^{10}}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{2^{(-15)}}$

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

Q. The value of ${\left(\right(2{)}^{-1})}^{-2}$ is .

1. $\frac{1}{4}$
2. 4
3. 16
4. $4^{-2}$

Q.

The value of ($4^{-7}$ ÷ $4^{-10}$ ) × $4^{-5}$ is ${16}^{-1}$.

1. True

2. False