Quotient Law

Q. If $a$ and $b$ are non-zero integers, $m$ and $n$ are any integers, then which of the following are true?

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

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.

Question 3(i)
Find the value of:

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

Q. Question 83 (xiii)

Multiply the following:
$b^3,3b^2,7a{b}^5$

Q. Prove that :

$\frac{a^{-1}}{a^{-1}+b^{-1}}+\frac{a^{-1}}{a^{-1}-b^{-1}}=\frac{2b^2}{b^2-a^2}$
[4 MARKS]

Q. $\frac{a^n}{b^n}=$ _____

1. $(\frac{a}{b}{)}^n$
2. $(\frac{a}{b}{)}^{-n}$
3. $\frac{a}{b^n}$
4. $\frac{a^n}{b}$

Q. Find the value of $4^{\frac{3}{2}}$ .
(2 marks)

Q.

Question 179(i)

Express each of the following in exponential form.
$\frac{-1296}{14641}$

Q. $\frac{\frac{2^2}{3^2}}{\frac{4^2}{5^2}}=$ ___

1. $\frac{25}{64}$
2. $\frac{64}{25}$
3. $\frac{25}{36}$
4. $\frac{36}{25}$

Q. Simplify : $\left[\right\{(-5{)}^5\times (-5{)}^{-10}\}÷2^5]\times {10}^5$

Q.

Question 84

In the following question, state whether the given statements are true (T) or false (F).

The exponential form for
$(-2{)}^4\times {\left(\frac{5}{2}\right)}^{4}is(5^4).$

Q.

Question 101

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

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

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

Q.

Question 179(iv)

Express each of the following in exponential form.
$\frac{-625}{10000}$

Q.

Question 179(ii)

Express each of the following in exponential form.
$\frac{-125}{343}$

Q. $\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}$ is equals to

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

1. $1$
2. $(a+b+c{)}^3$
3. $0$
4. $a^2+b^2+c^2$

Q. Which one of the following options is equal to the expression
${\left(\frac{3}{4}\right)}^5÷{\left(\frac{5}{3}\right)}^5?$

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

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

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

Q. What is the value of $\frac{{50}^2}{2^2\times 5^4}$?

1. $\frac{25}{4}$
2. $\frac{625}{100}$
3. $\frac{2500}{625}$
4. $1$

Q. The value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}$ is .

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

Q. The expression ${\left(x^{-2p}{y}^{3q}\right)}^6÷{\left(x^3{y}^{-1}\right)}^{-4p}$ after simplification becomes

1. independent of x but not of y
2. independent of both x and y
3. independent of y but not x
4. dependent of both x and y but independent of p and q

Q. ${\left(a^{10}\right)}^{10}{\left(a^6\right)}^{10}$=

Q.

Express the following algebraic fractions in the reduced from:

$$\frac{a^2-ab+b^2}{a^2+ab}÷\frac{a^3+b^3}{a^2-b^2}$$

Q.

$2^3\times 2^2=\_\_\_\_\_\_\_(2^{3+2}/2^{3\times 2})$

Q. The value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}$ is .

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

Q. The value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}$ is .

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

Q. Find the value of $\frac{\left(y^3-5y^2\right)}{y}\times \left(y-1\right)$

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

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

Q. If $a=2$ and $b=3,$ then find the values of each of the following:$(ab{)}^b$