Dividing Terms with the Same Exponent

Q. Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

1. $3^5$
2. $5\times 3\times 5$
3. $5^3$
4. 5

Q. Which of the following statements is true about the following graph?

1. The constant of proportionality can’t be determined.
   
2. The constant of proportionality is negative.
   
3. The constant of proportionality is positive.
   
4. The constant of proportionality is zero.
   

Q. The given graph shows the relationship between the cost of shirts $\left(y\right)$ vs. the number of shirts $\left(x\right)$.


Which of the following functions shows that the cost of each shirt is the same as that is shown on the graph.

1. $y=0.5x$
2. $y=12x$
3. $y=0.4x$
4. $y=10x$

Q. The given graph shows a proportional relationship between the number of tennis balls sold $\left(n\right)$ and their cost $\left(c\right)$. Which of the following statements about the graph are true?

I. The equation of the graph is $n=0.2c.$
II. The equation of the graph is $c=0.2n.$
III. Each tennis ball costs $\$5.$
IV. Each tennis ball costs $\$\mathrm{0.2.}$

1. Only statement IV.
2. Only statement I.
3. Both statement I and statement III.
4. Both statement II and statement IV.

Q. Two cars started from the same position on a straight road. The first car covers 35 miles in every 40 minutes, while the distance traveled by the second car with time is shown by the graph below.


What will be the distance between the cars after 2 hours from the start of their journey?

1. 90 miles
2. 20 miles
3. 105 miles
4. 15 miles

Q. Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

1. $5^3$
2. 5
3. $5\times 3\times 5$
4. $3^5$

Q.

Question 51

In the following question, fill in the blanks to make the statements true.

By multiplying ${\left(\frac{5}{3}\right)}^4$ by ___ we get $5^4$.

Q. On multiplying ___ by $3^{-5},$ we get $9^2$.

1. $3^7$
2. $3^{10}$
3. $3^9$
4. $3^8$

Q. Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

1. $5\times 3\times 5$
2. $3^5$
3. 5
4. $5^3$

Q. $\frac{\frac{p^x}{q^x}}{\frac{r^x}{s^x}}\times {\left(\frac{rq}{ps}\right)}^x=$ ___

1. 1
2. $(pqrs{)}^x$
3. ${\left(\frac{qr}{ps}\right)}^{2x}$
4. ${\left(\frac{ps}{qr}\right)}^{2x}$

Q. The given graph shows the number of teachers $\left(x\right)$ and the number of students $\left(y\right)$ in a class
Find the number of students for each teacher.

1. $15$
2. $40$
3. $10$
4. $20$

Q. The graph given below represents the proportional relationship between quantity $x$ and quantity $y$. Which of the following statement(s) is/are correct?

Q.

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

1. $\frac{4}{9}$

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

3. $\frac{9}{4}$

4. $\frac{-4}{9}$

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

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

Q. Person A and Person B start walking from the same initial position in different directions. What is the difference in their rate of walking in miles per hour based on the given graph?

1. $\frac{25}{76}\text{mi per h}$
2. $\frac{5}{36}\text{mi per h}$
3. $\frac{25}{46}\text{mi per h}$
4. $\frac{25}{36}\text{mi per h}$

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.

Simplify :$(\frac{1}{6^{-2}}-\frac{1}{3^{-3}})÷\frac{1}{5^{-2}}$

1. $(\frac{9}{25}{)}^2$

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

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

4. $(\frac{25}{9}{)}^2$

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

1. -1
2. \N
3. 1
4. 2

Q. For an equation of a proportional relationship in the form $y=mx$, choose the correct value(s) of $m$.

1. $m=$ Slope.
2. $m=$ Unit rate.
3. $m=$ Constant of proportionality
4. All of the above

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. Find the slope of the line $y=0.$

1. $0$
2. $1$
3. Not defined
4. $2$

Q. Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

1. $3^5$
2. $5\times 3\times 5$
3. 5
4. $5^3$

Q. Person A and Person B start walking from the same initial position in different directions. What is the difference in their rate of walking in miles per hour based on the given graph?

1. $\frac{25}{46}\text{mi per h}$
2. $\frac{25}{36}\text{mi per h}$
3. $\frac{5}{36}\text{mi per h}$
4. $\frac{25}{76}\text{mi per h}$

Q. Find the value of x, if:

$\left(\frac{125}{27}\right)\times (\frac{125}{27}{)}^x=(\frac{5}{3}{)}^{18}$

1. $5\times 3\times 5$
2. $3^5$
3. $5^3$
4. 5

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. Which of the following equations are correctly written?

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

Q.

The value of ${\frac{(-7)}{\left(7^6\right)}}^6$ is:

__

Q. Given below is a force-displacement graph. Calculate the force applied (in newtons) for a displacement of 10 meters based on the given graph. (Hint: Newton (N) is a unit of force and meter (m) is a unit of displacement.)

1. 5 N
2. 15 N
3. 10 N
4. 20 N