Test: Indices - Year 8 MCQ

Divide by 60 x 60 = 2⁴ x 3² x 5² to find the hours, then divide by 24 = 2³ x 3¹ to find days

• The number of days from 18th June to 15th July is 13 + 15 = 28 days.
• Since the plant doubles every 4 days, 28 divided by 4 is 7 doubling periods.
• The multiplication factor is 2⁷ = 128.
• Therefore the area is 20 x 128 = 2,560 cm².

To find what 0.2 raised to the power of 4 is as a power of 5, follow these steps:

• First, convert 0.2 into a fraction: 0.2 = 2/10 = 1/5.
• Next, calculate (1/5)⁴:
  • This means 1⁴ / 5⁴, which simplifies to 1 / 625.
• Now, express 625 as a power of 5:
  • 625 = 5⁴.
• Thus, 1 / 625 can be rewritten as 1 / 5⁴ = 5^-4.

Therefore, 0.2⁴ is equal to 5^-4.

After 1 year 500 x 1.015; after 3 years 500 x 1.015³

To find the index number that follows 3 to give 6,561, we need to understand the concept of index numbers.

• The expression can be written as 3 raised to the power of a certain number.
• We can express 6,561 as 3 raised to the power of 8, since 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 equals 6,561.
• This means that 8 is the index number we are looking for.

Therefore, the index number that follows 3 to give 6,561 is 8.

232³²³ means 2 multiplied by itself 3 times, which equals 8.

Convert 8³ to a power of 2 before adding the indices

5⁻² represents the reciprocal of 5² Therefore,

25³ ÷ 1,000 = 5⁶ ÷ 10³. Remember 1,000 cm³ = 1 litre

When multiplying powers with the same base, you add the exponents. Therefore,4³ × 4⁵ = 4³⁺⁵ = 4⁸