RBSE Class 8 Maths Important Questions Chapter 12 Exponents and Powers

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 12 Exponents and Powers Important Questions and Answers.

RBSE Class 8 Maths Chapter 12 Important Questions Exponents and Powers

Multiple Choice Questions:

Question 1.
Meaning of 2⁵ ÷ 2² is
(a) 2⁵⁺²
(b) 2^5-2
(c) 2^5/2
(d) (2⁵)²
Answer:
(b) 2^5-2

Question 2.
The value of 3° is
(a) 0
(b) 2
(c) 1
(d) 4
Answer:
(c) 1

Question 3.
The solution of \(\left(-\frac{8}{3}\right)^{24}\) is
(a) 3
(b) 8
(c) 24
(d) 2
Answer:
(c) 24

Question 4.
The solution of \(\left(\frac{1}{2^{-2}}\right)\) is
(a) 2
(b) 4
(c) \(\frac{1}{4}\)
(d) 1
Answer:
(b) 4

Question 5.
Simplification of (2 × 4)² is
(a) 2² × 4²
(b) 2²/4²
(c) 2² + 4²
(d) 4²/2²
Answer:
(a) 2² × 4²

Question 6.
Exponent form of (4)⁹ × (4)³ is
(a) (4)³
(b) (4)²⁷
(c) (4)¹²
(d) (4)⁶
Answer:
(c) (4)¹²

Question 7.
Solution of (3⁵ x 3³) ÷ (3)¹⁴ is:
(a) \(\frac{1}{3^{5}}\)
(b) \(\frac{1}{3^{6}}\)
(c) \(\frac{1}{3^{14}}\)
(d) \(\frac{1}{3^{3}}\)
Answer:
(b) \(\frac{1}{3^{6}}\)

Fill in the blanks:

Question 1.
Exponential form of \(\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4}\) is __________
Answer:
\(\left(\frac{3}{4}\right)^{3}\)

Question 2.
If a is a non zero rational number and n is a positive integer then a^-n = __________
Answer:
\(\frac{1}{a^{n}}\)

Question 3.
A number is called in __________ form if it is expressed in K × 10ⁿ, n = an integer
Answer:
Standard

Question 4.
In \(\left(\frac{4}{5}\right)^{50}\), then power is and base is __________
Answer:
50, \(\frac{4}{5}\)

Question 5.
Positive exponential form of 5^-2 is __________
Answer:
\(\left(\frac{1}{5^{2}}\right)\)

Very Short Answer Type Questions:

Question 1.
Write the exponential form of \(\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6}\)
Answer:
\(\left(\frac{5}{6}\right)^{4}\)

Question 2.
Write the exponential form of 729.
Answer:
729 = 3 × 3 × 3 × 3 × 3 × 3
= (3)⁶

Question 3.
Write the exponential form of \(\left(\frac{2}{5} \times \frac{2}{5} \times \frac{2}{5}\right) \times\left(\frac{3}{5} \times \frac{3}{5}\right)\)
Answer:
\(\left(\frac{2}{5}\right)^{3} \times\left(\frac{3}{5}\right)^{2}\)

Question 4.
Find the value of \(\left(\frac{1}{3}\right)^{3} \times\left(\frac{2}{3}\right)^{4}\)
Answer:
\(\left(\frac{1}{3}\right)^{3} \times\left(\frac{2}{3}\right)^{4}\)
= \(\left(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\right) \times\left(\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}\right)\)
= \(\frac{1}{27} \times \frac{16}{81}=\frac{16}{2187}\)

Question 5.
Write the exponential form of [(4³ × 4⁴) + 4⁹]².
Answer:
[(4³ × 4⁴) + 4⁹]²
= [(4³⁺⁴) + 4⁹]²
= (4⁷ ÷ 4⁹)²
= (4^7-9)² = (4^-2)²
= \(\left(\frac{1}{4^{2}}\right)^{2}=\frac{1}{4^{4}}\)

Short Answer Type questions:

Question 1.
The distance between Sun and Earth is 1496× 10⁸ m and the distance between Earth and Moon is 3.84 × 10⁸ m. During solar eclipse, moon comes in between Earth and Sun. At that time what is the distance between Moon and Sun.
Answer:
Distance between Sun and Earth = 1496 × 10⁸ m
Distance between Earth and Moon = 3.84 × 10⁸ m
Distance between. Sun and Moon
= 1496 × 10⁸ m - 3.84 × 10⁸ m
= (1496 - 3.84) × 10⁸ m
= 1492.16 × 10⁸ m