Simplify : \(\\ \cfrac { { 3 }^{ 2 } }{ { 3 }^{ -2 } } \)

Simplify and write the answer in exponential form:
\(\left( { 3 }^{ 5 }\div { 3 }^{ 8 } \right) ^{ 5 }\times { 3 }^{ -5 }\)

Find x so that (-7)^{x + 2} X( - 7) ⁵ = (-7) ¹⁰

Combine the scientific notations: (7 x 10 ²) (5.2 x 10⁷)

Write the following scientific notations in standard form: 2.27 \(\times\) 10^-4

Construct a rhombus ROSE with RO = 5 cm and RS = 8 cm. Also find its area.

Construct a rhombus NEST with NS = 9 cm and ET = 8 cm. Also find its area

Construct a rectangle BEAN with BE = 5 cm and BN = 3 cm. Also find its area

Construct a square LAMP of side 4 cm. Also find its area.

Draw a histogram for the following table which represents the age groups from 100 people in a village.

Ages	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Number of people	11	9	8	20	25	10	8	6	3

The following table gives the number of literate females in the age group 10 to 45 years in a town.

Age group	10-15	16-21	22-27	28-33	34-39	40-45
No. of females	350	920	850	480	230	200

Draw a histogram to represent the above data

Observe the given histogram and answer the following questions
Hint: Under weight: less than 30 kg; Normal weight: 30 to 45 kg; Obese: More than 45 kg
1. What information does the histogram represent?
2. Which group has maximum number of students?
3. How many of them are under weight?
4. How many students are obese?
5. How many students are in the weight group of 30-40 kg?

The following is the distribution of pocket money of 200 students in a school.

Pocket money	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Number of Students	25	40	33	28	30	20	16	8

Draw a frequency polygon using histogram.

Draw a frequency polygon for the following data using histogram

marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Number of students	5	8	10	18	25	22	20	13	6	3

Draw a frequency polygon for the following data without using histogram

Class interval (Marks)	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency	4	6	8	12	10	14	5	7