Quotient Law

Q.

Question 6(ii)
Evaluate:
${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$

Q. The value of the expression
$\frac{\left(0.3{)}^{\frac{1}{3}}{\left(\frac{1}{27}\right)}^{\frac{1}{4}}\right(9{)}^{\frac{1}{6}}(0.81{)}^{\frac{2}{3}}}{\left(0.9{)}^{\frac{2}{3}}\right(3{)}^{-\frac{1}{2}}{\left(\frac{1}{3}\right)}^{-2}(243{)}^{-\frac{1}{4}}}$

1. 0.3
2. 0.9
3. 1.27
4. 0.09

Q.

The expression ${\left(1+\frac{x^2}{2!}+\frac{x^4}{4!}+\frac{x^6}{6!}+...\right)}^2$ will be represented in ascending power of $x$ as

1. $1+\frac{2^2{x}^2}{2!}+\frac{2^4{x}^4}{4!}+.....$

2. $1+\frac{{\left(2x\right)}^2}{2!}+\frac{2^2{x}^4}{4!}+....$

3. $1+\frac{{\left(2x\right)}^2}{2.2!}+\frac{2x^4}{4!}+...$

4. $1+\frac{{\left(2x\right)}^2}{2.2!}+\frac{{\left(2x\right)}^4}{2.4!}+....$

Q.

Question 3(i)
Find the value of:

$(3^0+4^{-1})\times 2^2$

Q. $(1\times {10}^3)+(2\times {10}^2)+(3\times {10}^0)+(1\times {10}^{-1})+(2\times {10}^{-2})$=

1. $123.12$
2. $1230.12$
3. $1230.21$
4. $1230.21$

Q.

Simplify
$\frac{\left(0.3{)}^{\frac{1}{3}}{\left(\frac{1}{27}\right)}^{\frac{1}{4}}\right(9{)}^{\frac{1}{6}}(0.81{)}^{\frac{2}{3}}}{\left(0.9{)}^{\frac{2}{3}}\right(3{)}^{-\frac{1}{2}}{\left(\frac{1}{3}\right)}^{-2}(243{)}^{-\frac{1}{4}}}$

1. 0.3

2. 0.9

3. 1.27

4. 0.09

Q.

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

1. 3

2. 1

3. 4

4. 27

Q. If $\frac{\log 225}{\log 15}=\log x$, then the value $x$ is equal to

1. $120$
2. $65$
3. $95$
4. $100$

Q.

Simplify $2^5{5}^5$

1. 7⁵

2. 3⁵

3. 10⁵

4. 10¹⁰

Q.

Simplify ${(2^5÷2^8)}^5\times 2^{-5}$

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

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

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

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

Q.

$a^m$ ÷ $a^n$ = $a^{mn}$

1. True

2. False

Q.

If, $x={\left(\frac{-4}{5}\right)}^{30}÷{\left(\frac{-4}{5}\right)}^{28}$ and $y={\left(\frac{-4}{5}\right)}^2\times {\left(\frac{-4}{5}\right)}^3$, find the value of $(x^3÷y{)}^2$

1. $\frac{-16}{25}$

2. $\frac{6}{25}$

3. $\frac{16}{25}$

4. $\frac{6}{16}$

Q.

Solve : $14a{b}^{2}c{d}^2÷7a^{2}b{c}^{2}d$

Q. If $c^2+c=-1$ then the value of $c^3-1$ is

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

Q.

Simplify the following

$(4x^{2}y{z}^3-16x^3{y}^2{z}^2+12x^5{y}^7{z}^2)÷\left(2x^{2}y{z}^2\right)$

Q. If $a+b+c=9$ and $ab+bc+ac=26$. Find $a^2+b^2+c^2$.

Q. Simplify, giving answers with positive index:
$(4x^2{y}^3{)}^3÷(3x^2{y}^3{)}^3$

Q. Evaluate : $\frac{1}{a^0+b^0+c^0}$

1. $\frac{1}{a+b+c}$
2. 3
3. $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
4. $\frac{1}{3}$

Q. Given ${\log }_{10}a=b$, express ${10}^{2b-3}$ in terms of a.

Q. Simplify

1. $\sqrt[6]{6x^{14}{y}^7}$
2. $\sqrt[6]{6x^7{y}^7}$
3. $\sqrt[6]{6x^4{y}^7}$
4. $\sqrt[6]{6x^{14}{y}^3}$

Q.

Simplify :

(i) ${\left(\frac{x^a}{x^b}\right)}^{a^2+ab+b^2}\times {\left(\frac{x^b}{x^c}\right)}^{b^2+bc+c^2}\times {\left(\frac{x^c}{x^a}\right)}^{c^2+ca+a^2}$

(ii) ${\left(\frac{x^a}{x^{-b}}\right)}^{a^2-ab+b^2}\times {\left(\frac{x^b}{x^{-c}}\right)}^{b^2-bc+c^2}\times {\left(\frac{x^c}{x^{-a}}\right)}^{c^2-ca+a^2}$

Q.

Find the value of $x^{-3},ifx=(100{)}^{1-4}÷(100{)}^0.$

1. ${100}^9$

2. ${100}^8$

3. ${100}^7$

4. ${100}^6$

Q. Choose the correct answer from the given four options:
The value of $\frac{{10}^{22}+{10}^{20}}{{10}^{20}}$ is

1. $10$
2. ${10}^{22}$
3. ${10}^{42}$
4. $101$

Q. Simplify $(p-2q+r{)}^2-(-p+2q-r{)}^2$

Q. Simplify:
${\left(\frac{x^a}{x^b}\right)}^{a^2+ab+b^2}\times {\left(\frac{x^b}{x^c}\right)}^{b^2+bc+c^2}\times {\left(\frac{x^c}{x^a}\right)}^{c^2+ca+a^2}$