Class 8 Maths: Exponential Notation and Operations — Practice Questions with Answers

Explanation: 3⁴ means 3 multiplied by itself 4 times: 3 × 3 × 3 × 3. Step by step, 3 × 3 = 9, then 9 × 3 = 27, then 27 × 3 = 81. The answer 12 comes from wrongly multiplying the base and the exponent as 3 × 4.

Explanation: Break 125 into equal factors: 125 = 5 × 25 = 5 × 5 × 5. Since 5 is multiplied 3 times, 125 = 5³. The option 3⁵ swaps the base and exponent and equals 243, while 5² = 25 and 25² = 625.

Explanation: When powers with the same base are multiplied, the exponents are added: 2⁵ × 2³ = 2⁵⁺³ = 2⁸. Check: 32 × 8 = 256, and 2⁸ = 256. Choosing 2¹⁵ is the common error of multiplying the exponents, and 4⁸ wrongly multiplies the bases.

Explanation: Any non-zero number raised to the power 0 equals 1, so 7⁰ = 1. You can see this from the pattern 7³ = 343, 7² = 49, 7¹ = 7, where each step divides by 7, and 7 ÷ 7 = 1. It is not 0, because the pattern divides by 7 at each step rather than falling to zero.

Explanation: For a power raised to another power, multiply the exponents: (2³)² = 2⁶ = 64. You can also check directly: 2³ = 8 and 8² = 64. Choosing 32 comes from adding the exponents to get 2⁵ instead of multiplying them.

Explanation: A negative exponent means the reciprocal of the positive power: 5⁻² = 1 ÷ 5² = 1/25. The minus sign in the exponent does not make the value negative, so −25 is wrong. It only makes the value a fraction smaller than 1.

Explanation: In standard form a number is written as a number between 1 and 10 multiplied by a power of 10. Starting from 0.00046, the decimal point must move 4 places to the right to reach 4.6, so 0.00046 = 4.6 × 10⁻⁴. Counting 5 places and choosing 10⁻⁵ is the common slip; count only until the point sits just after the first non-zero digit.

Explanation: When dividing powers with the same base, subtract the exponents: 3⁸ ÷ 3⁵ = 3⁸⁻⁵ = 3³. Then 3³ = 3 × 3 × 3 = 27. Picking 81 or 243 comes from a wrong subtraction, since 3⁴ = 81 and 3⁵ = 243.

Explanation: Work out each value: 10² = 100, 5³ = 125, 3⁵ = 243 and 2¹⁰ = 1024. So 2¹⁰ is the greatest even though its base is the smallest. A small base with a large exponent can beat a large base with a small exponent, because repeated doubling grows very fast.

Explanation: First apply the power-of-a-power rule: (5²)³ = 5⁶. Then 5⁶ × 5⁴ = 5¹⁰, and 5¹⁰ ÷ 5⁸ = 5², since 10 − 8 = 2. So the value is 5² = 25. The answer 1 would need all the exponents to cancel, but 6 + 4 − 8 = 2, not 0.

Explanation: Write 243 as a power of 3: 243 = 3 × 3 × 3 × 3 × 3 = 3⁵. Since 3ˣ⁺² = 3⁵ and the bases are equal, the exponents must be equal, so x + 2 = 5. Therefore x = 3. Choosing 5 forgets to subtract the 2 from the exponent.

Explanation: Divide the two lengths: 10⁻⁵ ÷ 10⁻⁷. Subtracting the exponents gives −5 − (−7) = 2, so the quotient is 10² = 100. Choosing 1/100 comes from dividing the wrong way round: the bacterium is the longer one because −5 is greater than −7.