CBSE Class 8 Maths Exponents and powers HOTs

HOTS

Question. Find the missing number x in : 5² + x² = 13²
Answer : 12

Question. Find 724.9 × 10³ in usual form.
Answer : 724900

Question. Find the value of (125)².
Answer : 15625

Question. Find 326800 in standard form.
Answer : 3.268 × 105

Question. Simplify in exponent form (2^–3 x 2⁶) 2⁵ .
Answer : 2^–2

Question. Find 0.000000 375 in standard form.
Answer : 3.75 × 10–7

Question. Find the value of (2/3)^-4
Answer : 81/16

Question. Find 87.34 × 10^–3 in standard form
Answer : 8.734 × 10^–2

Question. Find 72.48 × 10³ in standard form.
Answer : 7.248 × 10⁴

Question. Find in the form of positive exponent (x^–4)³
Answer : 1/x¹²

Question. Find the value of 6⁷ - 6⁹ / 6⁵
Answer : –1260

Question. Find 3.72 × 10^–2 in usual form.
Answer : 0.0372

Question. Find the value of (3/-2)² x (-2/3)³
Answer : -2/3

Question. Simplify in exponent form. (a⁷ a^–5) × a^–2.
Answer : a10

Question. Simplify :

Answer : 9/25

Question. Which number is greater : 10^–49 or 2×10^–50 and by how much?
Answer : 10^–49, 8×10^–50

Question.

Answer : 7/16

2. If a^x=c^q=b and c^y=a^z=d, prove that xy=qz.

3. If a is a non-zero natural number, prove that (a^x–y)x+y × (a^y–z)y+z × (a^z–x)z+x=1.

CHALLENGES

1. What is the least positive value of 't' such that 25 x t-4/5-3 x 10 x t-8 is an integer. Find all the other values of 't' to suit the given condition.

2. Find the value of 

3. Suppose a^2a=(2a)^a, for some positive integer 'a'. Prove that a=2. 

4. Simplify : 

5. Simplify: (a+b+c)(a^–1+b^–1+c^–1)–a^–1b^–1c^–1(b+c)(c+a)(a+b).

6. If 2x+1–2x=8, find the value of x.

7. Find x, if 3^x+5 = 3^x+3 + 8/9 .

8. If a^x=b, b^y=c and c^z=a, prove that xyz=1. 

9. If 4^x+4^–x=16 1/16 , find x.

SUMMARY

1. Repeated multiplication can be written in the form of exponents. The number which is repeated is called base and the number of times it is repeated is called power.

2. Laws of exponents.
If a and b are two non - zero rational numbers and m, n are any two integers, then 

3. A number is said to be in the standard form if it is expressed as k×10n, where k is 1≤x<10 and n is an integer.

4. Conversion of numbers into the standard form and the standard form into numbers.

ERRORANALYSIS

1. x³.x² is written as x⁶ instead of x⁵

2. x⁸÷x² is written as x⁴ instead of x⁶

3. (x³)² is written as x³² instead of x⁶

4. 5x^-1 is written as 1/5x instead of 5/x

5. (2y^-4/x)^-3 is written as (x/2y⁴)³ instead of (x/2y^-4)³

6. When a decimal is expressed in the standard form, the power of 10 is the negative power.

ACTIVITY I

Crossword  

Across

Question. In x^m × xⁿ = x^p, p is the ______ of m and n.
Answer: Sum

Question. Very large numbers like 6,250,000,000 can be conveniently written using ______.
Answer: Exponents

Question. The value of an, if n=0 is ______.
Answer: One

Question. Very small numbers can be expressed in the standard form using _______exponents.
Answer: Negative

Down

Question. The value of 3^–2
Answer: One-ninth

Question. The value of 1/2^-3
Answer: Eight

Question. 57 is read as 5 raised to the___________of 7.
Answer: Power

Question. a–m is the ____________inverse of a^m.
Answer: Multiplicative

Question. 1.24 × 10^-4 is known as the ___________form of 0.000124.
Answer: Standard