Class 8 Maths Chapter 10 HOTS Questions - Exponents and Powers

Q1: Express the the mean distance between Earth and moon is 384,000,000 m in standard from.
Ans: Standard form of 3,84,000,000 is 3.84×10⁸

Q2: Express the number appearing in the following statement in standard from:
The distance between Sun and Saturn is 1,433,000,000,000 m .
Ans: Standard form of 1,433,000,000,000 is 1.433×10¹² .

Q3: Write the base and the exponent of (7x)²
Ans: Given the number is (7x)².
So the base is 7x and the exponent is 2.

Q4: Write the given statement in the product form.x³ y⁴.
Ans: We know that,
b³ = b×b×b.
Similarly,
x³ =x×x×x.
y⁴ =y×y×y×y.
Thus,
x3 y⁴ =x×x×x×y×y×y×y.

Q5: Write 629000 in standard form.
Ans:
629000=6.29×100000
=6.29×10⁵

Q6: Identify the greater number among the two numbers:
2¹⁰  or 10²
Ans:
2¹⁰ =2×2×2×2×2×2×2×2×2×2=1,024
10² =10×10=100
Since, 1,024>100
Thus, 2¹⁰ >10²

Q7: Change the given number into it's standard form
128000000
Ans: 128000000=128×10⁶
=12.8×10×10⁶
1.28×10×10×10⁶
=1.28×10⁸

Q8: Identify the greater number between the following:
4³  or 3⁴
Ans: 4³ or 34 ⇒ 4³=4×4×4=164
⇒3⁴=3×3×3×3=81
∴3⁴>4³

 Q9: Evaluate:
Ans:
Here we have,

Q10: Evaluate:

Ans:

Q11: Express the number appearing in the following statement in standard from.
Diameter of the sun is 1,400,000,000 m
Ans: Diameter of sun =1,400,000,000 m
In standard form,
⇒ Diameter of sun =(1.4×10⁹) m

Q12: Simplify
[(2)⁻¹+(4)⁻¹+(3)⁻¹]⁻¹
Ans:
Let us simplify the given expression
[(2) ⁻¹ +(4) −1 +(3) ⁻¹ ] −1 =[(1/2)+(1/4)+(1/3)] ⁻¹
=[(6+3+4)/12] ⁻¹
=[13/12] ⁻¹
=12/13

Q13: Evaluate:
(0.25) ⁻¹.
Ans:

Q14: Evaluate:
Ans: Here we have

Q15: Evaluate:
 
Ans: