Division of Exponents Having the Same Base

Q. The distance between Earth and the sun is approximately 150 million kilometres and between Uranus and the sun is approximately 3 billion kilometres.
Thus, the distance between Uranus and the sun is ___ times the distance between Earth and the sun.

1. 2
2. 20
3. 0.5
4. 200

Q. Express in power notation.

$\text{(a)}\frac{49}{81}\text{(b)}\frac{-8}{27}$

Q. If $x$ be any integer different from zero and $m$ be any positive integer, then $x^{-m}$ is equal to

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

Q.

Question 84 (iii)

Simplify

${(\frac{7}{9}a+\frac{9}{7}b)}^2-ab$

Q.

The distance between two planets is 2.496×${10}^{11}$ m and the distance between two stars is 4.84×${10}^8$ m . Calculate the difference of these distances in metres.

Q. Solve the given expression by substituting the value of x = 6 in $\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Q. Simplify: $\frac{35m^3}{7m^2}$

1. 5 m
2. $\frac{1}{5m}$
3. $\frac{m}{5}$
4. $\frac{5}{m}$

Q.

Question 180(vi)

Simplify :
$\frac{(3^{-2}{)}^2\times (5^2{)}^{-3}\times (t^{-3}{)}^2}{(3^{-2}{)}^5\times (5^3{)}^{(-2)}\times (t^{-4}{)}^3}$

Q. If $a^7=3$, find the value of $\frac{{\left(a^{-2}\right)}^{-3}\times {\left(a^3\right)}^4\times {\left(a^{-17}\right)}^{-1}}{a^7}$

Q. Evaluate the expression $(-x{)}^3\times (-x{)}^2$ for $x=\frac{2}{3}.$

1. $-\frac{32}{27}$
2. $\frac{64}{81}$
3. $-\frac{32}{243}$
4. $\frac{32}{81}$

Q. Express in power notation.

$\text{(a)}\frac{49}{81}\text{(b)}\frac{-8}{27}$

Q. Question 6(i)
Evaluate:
${\{{\left(\frac{1}{3}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\}}^{-1}$

Q. Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Q. $(30{)}^{-24}$ =

1. $6^{-24}\times 5^{-24}$
2. $2^{-24}\times {15}^{-24}$
3. $2^{-48}\times {15}^{-24}$
4. $3^{-48}\times {10}^{-24}$

Q.

$1c{m}^3=\_\_\_\_\_\_m^3.$

Q. ${(-\frac{5}{7})}^{-5}$ is equal to

1. ${\left(\frac{7}{5}\right)}^5$
2. ${\left(\frac{5}{7}\right)}^5$
3. ${\left(\frac{5}{7}\right)}^{-5}$
4. ${(-\frac{7}{5})}^5$

Q. If $x$ be any integer different from zero and $m,n$ be any integers, then ${\left(x^m\right)}^n$ is equal to

1. $x^{m-n}$
2. $x^{m+n}$
3. $x^{mn}$
4. $x^{\frac{m}{n}}$

Q.

Simplify: $\frac{(-2{)}^3\times (-2{)}^7}{3\times 4^6}$

1. 12

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

3. 11

4. $\frac{1}{14}$

Q. Express the following in expanded from.
$6.324\times {10}^{-6}$

Q. Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Q. Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Q. Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$

Q. Solve for x = 6.
$\frac{\left(45x^{-4}\right)}{(5^{-4}\times {10}^2\times x^{-8})}$