Comparison of Quantities Using Exponents

Q. Find the value of $x,$ if $5^{x-3}\times 3^{2x-8}=225$.

Q. The usual form of $1.05\times {10}^{-6}$ is:

1. $1050000$
2. $10500$
3. $0.00000105$
4. $0.00105$

Q.

Question 4(i)
Identify the greater number, wherever possible, in each of the following:
(i) $4^{3}and{3}^4$

Q.

Question 45

State whether the given statements are true or false
$3^4>4^3$

Q. If ${\left(\frac{x^m\times x^n}{x^p}\right)}^q=x^K$ then what is the value of K?

1. (m + n + q)
2. (m + n - p)q
3. (m + n) (n + q)
4. (pq) (mn)

Q.

Superman can fly at speeds almost equal to $2.6\times {10}^7$ m/s. A supersonic jet on the planet Krypton can fly at a maximum speed of 130000 m/s. Choose the correct option(s):

1. Superman flies 2000 times faster than the jet

2. The jet flies 200 times faster than Superman

3. The jet flies 2000 times faster than Superman

4. Superman flies 200 times faster than the jet

Q. Between $2^{10}$ and ${10}^2$ , which one is greater?

Q.

Each of the numbers 1, 2, 3 and 4 is substituted, in some order for p, q, r and s. The greatest possible value of $p^q+r^s$ is:

1. 83
2. 81
3. 84
4. 82

Q.

Simplify [2 MARKS]

$2^5\times 3\times 4^2\times 5$

Q.

The value of $({\left(2^2\right)}^2{)}^2$ is:

1. $2^{16}$

2. $2^8$

3. $2^6$

4. $2^4$

Q.

Between $2^{10}$ and ${10}^2$ , ${10}^2$ is greater.

1. True

2. False

Q. Comparing 2 numbers x and y we find that x is 1500 times that of y. If x = $3\times {10}^6$, then y = $2\times {10}^4$

1. False
2. True

Q. If $\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$ then the value of ${\left(\frac{q}{p}\right)}^3$ is-

1. $\frac{28}{54}$
2. $\frac{54}{28}$
3. $\frac{729}{64}$
4. $\frac{64}{729}$

Q. $1^{2018}$ >

1. $1^{2017}$
2. $1^{-2018}$
3. $(-1{)}^{2018}$
4. $(-1{)}^{2017}$

Q.

Each of the numbers 1, 2, 3 and 4 is substituted, in some order for p, q, r and s. The greatest possible value of $p^q+r^s$ is:

1. 82
2. 81
3. 83
4. 84

Q. Solve:$2^{2x+3}+1=3^2{2}^x$

Q. Superman flies at a speed of $2.6\times {10}^7$ m/s . If the speed of a jet is 130000 m/s, then Superman's speed is times the speed of the jet.

1. 200
2. 2000
3. 240
4. 2400

Q. Which is greater:
(i) $2^3$ or $3^2$
(ii) $2^5$ or $5^2$

Q. The speed of light =$3\times {10}^{8}m/s$
The speed of sound =$3.43\times {10}^{2}m/s$
The speed of light is almost ${10}^6$ times that of sound

1. True
2. False

Q. Write the given product in exponential form.
$5\times a\times a\times a\times b\times b\times c\times c\times c$.

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

1. ${\left(y^{\frac{2}{3}}\right)}^9$
2. ${\left(\sqrt{y^6}\right)}^2$
3. ${\left(y^{\frac{1}{3}}\right)}^{12}$
4. $\sqrt[3]{3y^{18}}$

Q.

Q. Identify the greater number in each of the following: $3^4$ or $4^3$

Q.

$3^4$ is greater than $4^3.$

1. True

2. False

Q. If a = $8\times {10}^3$ and b =$4\times {10}^{-2}$ then ratio a : b = 200000 : 1

1. True
2. False

Q. If $\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$ then the value of ${\left(\frac{q}{p}\right)}^3$ is-

1. $\frac{28}{54}$
2. $\frac{729}{64}$
3. $\frac{64}{729}$
4. $\frac{54}{28}$

Q. if ${\left(\frac{9}{4}\right)}^{-4}\times {\left(\frac{2}{3}\right)}^3={\left(\frac{p}{q}\right)}^{11}$, then find the value of${\left(\frac{p}{q}\right)}^{-2}$.

Q. Select the following expression(s) which is(are) equal to $16\times 2^4.$

1. $2^4\times 2^4$
2. $2^8$
3. $512$
4. $256$

Q. 120 = 2³ ×3 × 5

1. True
2. False

Q. Identify the greater number:
$5^{3}or{3}^5$ (2 marks)