DAV Class 7 Maths Chapter 4 Worksheet 3 Solutions

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The DAV Class 7 Maths Solutions and DAV Class 7 Maths Chapter 4 Worksheet 3 Solutions of Application of Percentage offer comprehensive answers to textbook questions.

DAV Class 7 Maths Ch 4 WS 3 Solutions

Question 1.
Which of the following are true?
(i) \(\left(+\frac{3}{4}\right)^3 \times\left(\frac{-3}{4}\right)^3=\left(\frac{-3}{4}\right)^6\)
Answer:
\(\left(+\frac{3}{4}\right)^3 \times\left(\frac{-3}{4}\right)^3=\left(\frac{-3}{4}\right)^6\)
Here bases are not same
∴ it is false.

(ii) \(\left(\frac{4}{7}\right)^5 \times\left(\frac{4}{7}\right)^3=\left(\frac{4}{7}\right)^8\)
Answer:
\(\left(\frac{4}{7}\right)^5 \times\left(\frac{4}{7}\right)^3=\left(\frac{4}{7}\right)^8\)
⇒ \(\left(\frac{4}{7}\right)^{5+3}=\left(\frac{4}{7}\right)^8\)
⇒ \(\left(\frac{4}{7}\right)^8=\left(\frac{4}{7}\right)^8\)
Hence it is true.

(iii) \(\left(\frac{-1}{2}\right)^4 \div\left(\frac{-1}{2}\right)^3=\left(\frac{-1}{2}\right)\)
Answer:
\(\left(\frac{-1}{2}\right)^4 \div\left(\frac{-1}{2}\right)^3=\left(\frac{-1}{2}\right)\)
⇒ \(\left(\frac{-1}{2}\right)^{4-3}=\left(\frac{-1}{2}\right)\)
⇒ \(\left(\frac{-1}{2}\right)=\left(\frac{-1}{2}\right)\)
Hence it is true.

(iv) \(\left(\frac{6}{7}\right)^6 \div\left(\frac{6}{7}\right)^0=\left(\frac{6}{7}\right)^0\)
Answer:
\(\)
⇒ \(\left(\frac{6}{7}\right)^{6-0}=\left(\frac{6}{7}\right)^0\)
⇒ \(\left(\frac{6}{7}\right)^6 \neq\left(\frac{6}{7}\right)^0\)
Hence it is false.

DAV Class 7 Maths Chapter 4 Worksheet 3 Solutions

Questions 2.
Fill in the blanks in each of the following so as to make the statements true:
(i) \(\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right)^3=\left(\frac{-2}{3}\right)^{\cdots}\)
Answer:
\(\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right)^3=\left(\frac{-2}{3}\right)\)
⇒ \(\left(\frac{-2}{3}\right)^{1+3}=\left(\frac{-2}{3}\right)^4\)
∴ (…………..) = 4

(ii) \(\left(\frac{4}{5}\right)^{\cdots} \times\left(\frac{4}{5}\right)^9=\left(\frac{4}{5}\right)^{11}\)
Answer:
\(\left(\frac{4}{5}\right)^{\cdots} \times\left(\frac{4}{5}\right)^9=\left(\frac{4}{5}\right)^{11}\)
⇒ \(\left(\frac{4}{5}\right)^{\cdots}=\left(\frac{4}{5}\right)^{11} \div\left(\frac{4}{9}\right)^9\)
⇒ \(\left(\frac{4}{5}\right)^{\cdots}=\left(\frac{4}{5}\right)^{11-9}\)
⇒ \(\left(\frac{4}{5}\right)^2=\left(\frac{4}{5}\right)^2\)
∴ (…………..) = 2

(iii) \(\left(\frac{-3}{7}\right)^{15} \div\left(\frac{-3}{7}\right)^{\cdots}=\left(\frac{-3}{7}\right)\)
Answer:
\(\left(\frac{-3}{7}\right)^{15} \div\left(\frac{-3}{7}\right)^{\cdots}=\left(\frac{-3}{7}\right)\)
⇒ \(\left(\frac{-3}{7}\right)^{15} \div\left(\frac{-2}{3}\right)=\left(\frac{-3}{7}\right)^{\cdots}\)
⇒ \(\left(\frac{-3}{7}\right)^{15-1}=\left(\frac{-3}{7}\right)^{\cdots}\)
⇒ \(\left(\frac{-3}{7}\right)^{14}=\left(\frac{-3}{7}\right)^{-1}\)
∴ (…………..) = 14

(iv) \(\left(\frac{-1}{10}\right)^{\cdots} \div\left(\frac{-1}{10}\right)^8=\left(\frac{-1}{10}\right)^8\)
Answer:
\(\left(\frac{-1}{10}\right)^{\cdots} \div\left(\frac{-1}{10}\right)^8=\left(\frac{-1}{10}\right)^8\)
⇒ \(\left(\frac{-1}{10}\right)^{\cdots}=\left(\frac{-1}{10}\right)^8 \times\left(\frac{-1}{10}\right)^8\)
⇒ \(\left(\frac{-1}{10}\right)^{\cdots}=\left(\frac{-1}{10}\right)^{8+8}\)
⇒ \(\left(\frac{-1}{10}\right)^{\cdots}=\left(\frac{-1}{10}\right)^{16}\)
∴ (…………..) = 16

(v) \(\left(\frac{2}{9}\right)^6 \div\left(\frac{2}{9}\right)^0=\left(\frac{2}{9}\right)^{\cdots}\)
Answer:
\(\left(\frac{2}{9}\right)^6 \div\left(\frac{2}{9}\right)^0=\left(\frac{2}{9}\right)^{\cdots}\)
⇒ \(\left(\frac{2}{9}\right)^{6-0}=\left(\frac{2}{9}\right)^{\cdots}\)
⇒ \(\left(\frac{2}{9}\right)^6=\left(\frac{2}{9}\right)^3\)
∴ (…………..) = 6

(vi) \(\left(\frac{-12}{13}\right)^2 \times\left(\frac{-12}{13}\right)^{\cdots}=\left(\frac{-12}{13}\right)^5\)
Answer:
\(\left(\frac{-12}{13}\right)^2 \times\left(\frac{-12}{13}\right)^{\cdots}=\left(\frac{-12}{13}\right)^5\)
⇒ \(\left(\frac{-12}{13}\right)^{\cdots}=\left(\frac{-12}{13}\right)^5 \div\left(\frac{-12}{13}\right)^2\)
⇒ \(\left(\frac{-12}{13}\right)=\left(\frac{-12}{13}\right)^{5-2}\)
⇒ \(\left(\frac{-12}{13}\right)^{\cdots}=\left(\frac{-12}{13}\right)^3\)
∴ (…………..) = 3

Question 3.
Simplify and express the result in exponential form:
(i) \(\left(\frac{-3}{7}\right)^3 \times\left(\frac{-3}{7}\right)^4\)
Answer:
\(\left(\frac{-3}{7}\right)^3 \times\left(\frac{-3}{7}\right)^4\)
= \(\left(\frac{-3}{4}\right)^{3+4}=\left(\frac{-3}{4}\right)^7\)

(ii) \(\left(\frac{11}{12}\right)^{15} \times\left(\frac{11}{12}\right)^5 \times\left(\frac{11}{12}\right)^{10}\)
Answer:
\(\left(\frac{11}{12}\right)^{15} \times\left(\frac{11}{12}\right)^5 \times\left(\frac{11}{12}\right)^{10}\)
⇒ \(\left(\frac{11}{12}\right)^{15+5+10}=\left(\frac{11}{12}\right)^{30}\)

(iii) \(\left(\frac{-9}{11}\right)^9 \div\left(\frac{-9}{11}\right)^7\)
Answer:
\(\left(\frac{-9}{11}\right)^9 \div\left(\frac{-9}{11}\right)^7\)
= \(\left(\frac{-9}{11}\right)^{9-7}=\left(\frac{-9}{11}\right)^2\)

(iv) \(\left(\frac{1}{4}\right)^8 \div\left(\frac{1}{4}\right)^6\)
Answer:
\(\left(\frac{1}{4}\right)^8 \div\left(\frac{1}{4}\right)^6\)
= \(\left(\frac{1}{4}\right)^{8-6}=\left(\frac{1}{4}\right)^2\)

(v) \(\left(\frac{15}{19}\right)^{35} \div\left(\frac{15}{19}\right)^{24}\)
Answer:
\(\left(\frac{15}{19}\right)^{35} \div\left(\frac{15}{19}\right)^{24}\)
= \(\left(\frac{15}{19}\right)^{35-24}=\left(\frac{15}{19}\right)^{11}\)

Question 4.
Simplify and express the results as a rational number.
(i) \(\left(\frac{5}{7}\right)^4 \div\left(\frac{5}{7}\right)^2\)
Answer:
\(\left(\frac{5}{7}\right)^4 \div\left(\frac{5}{7}\right)^2=\left(\frac{5}{7}\right)^{4-2}\)
= \(\left(\frac{5}{7}\right)^2=\frac{5}{7} \times \frac{5}{7}\)
= \(\frac{25}{49}\)

(ii) \(\left(\frac{-2}{3}\right)^2 \times\left(\frac{-2}{3}\right)^3\)
Answer:
\(\left(\frac{-2}{3}\right)^2 \times\left(\frac{-2}{3}\right)^3=\left(\frac{-2}{3}\right)^{2+3}\)
= \(\left(\frac{-2}{3}\right)^5=\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right) \times\left(\frac{-2}{3}\right)\)
= \(\frac{-32}{243}\)

(iii) \(\left(\frac{3}{4}\right)^3 \times\left(\frac{3}{4}\right)^2\)
Answer:
\(\left(\frac{3}{4}\right)^3 \times\left(\frac{3}{4}\right)^2=\left(\frac{3}{4}\right)^{3+2}\)
= \(\left(\frac{3}{4}\right)^5\)
= \(\frac{243}{1024}\)

(iv) \(\left(\frac{-3}{5}\right)^6 \div\left(\frac{-3}{5}\right)^3\)
Answer:
\(\left(\frac{-3}{5}\right)^6 \div\left(\frac{-3}{5}\right)^2=\left(\frac{-3}{5}\right)^{6-2}\)
= \(\left(\frac{-3}{5}\right)^4\)
= \(\frac{81}{625}\)

(v) \(\left(\frac{-1}{10}\right)^4 \times\left(\frac{-1}{10}\right)^2\)
Answer:
\(\left(\frac{-1}{10}\right)^4 \times\left(\frac{-1}{10}\right)^2=\left(\frac{-1}{10}\right)^{4+2}\)
= \(\left(\frac{-1}{10}\right)^6\)
= \(\frac{1}{1000000}\)

DAV Class 7 Maths Chapter 4 Worksheet 3 Solutions

Question 5.
Evaluate:
(i) \(\left(\frac{3}{4}\right)^3 \times\left(\frac{2}{3}\right)^2\)
Answer:
\(\left(\frac{3}{4}\right)^3 \times\left(\frac{2}{3}\right)^2\)
DAV Class 7 Maths Chapter 4 Worksheet 3 Solutions 1
= \(\frac{3}{16}\)

(ii) \(\left[\left(\frac{1}{3}\right)^6 \div\left(\frac{1}{3}\right)^5\right] \div \frac{1}{3}\)
Answer:
\(\left[\left(\frac{1}{3}\right)^6 \div\left(\frac{1}{3}\right)^5\right] \div\left(\frac{1}{3}\right)\)
= \(\left(\frac{1}{3}\right)^{6-5} \div \frac{1}{3}=\frac{1}{3} \div \frac{1}{3}\)
= 1

(iii) (24 × 25) ÷ 28
Answer:
= 24+5 ÷ 28
= 29 ÷ 28
= 29-8
= 2

(iv) [42 – 32] ÷ \(\left(\frac{1}{7}\right)^2\)
Answer:
= (16 – 9) ÷ \(\left(\frac{1}{7}\right)^2\)
= (7) ÷ (7)-2
= 71+2
= 73
= 343.