Important Questions: Exponents and Powers - Class 7 MCQ

The expression for (-2a) raised to the power of 3 can be simplified as follows:

• Step 1: Apply the exponent: (-2a)³ = (-2)³ × a³
• Step 2: Calculate (-2)³: This equals -8.
• Step 3: Combine the results: -8 × a³

Therefore, the final result is:

(-2a)³ = -8a³

(2² × 2)² = (2²⁺¹)² = (2³)² = 2^3×2 = 2⁶

Option A: Both sides equal 1 because any non-zero number raised to the power of 0 is 1. Thus, this statement is true.

Option B: Using exponent rules:

• 10² × 10⁸ = 10²⁺⁸ = 10¹⁰, not 10¹⁶.
• So, it's false.

Option C: Calculating gives:

• 4 × 27 = 108, not 65.
• Hence, false.

Option D: Here, we have:

• 2³ = 8
• 3² = 9
• Since 8 is less than 9, this is false.

Only option A is correct.

To solve the expression 3⁰ + 4⁰ + 5⁰, we use the property that any non-zero number raised to the power of zero equals 1. Therefore, each term simplifies as follows:

• 3⁰ = 1
• 4⁰ = 1
• 5⁰ = 1

Adding these together gives:

1 + 1 + 1 = 3. Thus, the correct answer is C.

(2⁰ + 3⁰) × 4⁰ =

To solve the expression, we apply the rule that any number raised to the power of zero equals 1. Therefore:

• 2⁰ = 1
• 3⁰ = 1
• 4⁰ = 1

Now, substituting these values into the expression:

(1 + 1) × 1 = 2

Thus, the final answer is 2.

Any non-zero number raised to the power of 0 is equal to 1. Therefore:

• 3⁰ = 1
• 4⁰ = 1
• 5⁰ = 1

Multiplying these together:

• 1 × 1 × 1 = 1

Thus, the correct answer is A.

Using the power of a power rule, the following formula applies:

(a^m)ⁿ = a^(m×n)

Applying this rule, we can simplify:

• (5²)¹⁰ becomes 5^(2×10)
• This further simplifies to 5²⁰

To solve (-5)⁴, we can break it down into steps:

• First, calculate (-5) × (-5):

(-5) × (-5) = 25

• Next, take the result and multiply by (-5):

25 × (-5) = -125

• Finally, multiply this result by (-5):

-125 × (-5) = 625

Therefore, (-5)⁴ equals 625.

When dividing powers of the same base, you need to subtract the exponents. Here’s how it works:

• Base: In this example, the base is 10.
• Exponents: The exponents involved are 6 and 5.
• To divide the powers:
• Start with the expression: 10⁶ ÷ 10⁵
• Subtract the exponents: 6 - 5
• The result is: 10¹

Therefore, 10⁶ ÷ 10⁵ = 10¹.

When multiplying exponents with the same base, you need to add their powers. Here’s how it works:

• Start with the base: -3
• Look at the exponents: 4 and 6
• Perform the addition: 4 + 6 = 10

Putting this together, you get:

(-3)⁴ × (-3)⁶ = (-3)⁽⁴⁺⁶⁾ = (-3)¹⁰

Thus, the final result is ? = 10.

To solve the equation 2³ × 2⁴ = 2^?, we use the rule of exponents which states that when multiplying powers with the same base, you add the exponents. Therefore:

• 2³ × 2⁴ = 2³⁺⁴
• This simplifies to 2⁷.

Thus, the value of ? is:

• ? = 7

The calculation can be broken down into the following steps:

• Step 1: Calculate (-2) × (-2) which equals 4.
• Step 2: Next, calculate 4 × (-2) which results in -8.
• Step 3: Finally, calculate -8 × (-2) yielding 16.

Therefore, the expression (-2)4 equals 16.

The value of any non-zero number raised to the power of 0 is always 1. Therefore:

• 9⁰ = 1

The number 1000 can be expressed as:

• 10 × 10 × 10

This is equivalent to:

• 10³

Therefore, the exponential form of 1000 is:

• 10³

To find the exponential form of 625, express it as a power of 5. Here are the steps:

• Calculate: 5 × 5 = 25 (which is 5²)
• Then, 25 × 5 = 125 (which is 5³)
• Finally, 125 × 5 = 625 (which is 5⁴)

Therefore, the exponential form of 625 is 5⁴.

To express 64 in exponential form, we recognise that 64 can be written as a power of 2. By multiplying 2 by itself six times, we get:

• 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

Therefore, the exponential form of 64 is 2⁶, which corresponds to option B.

To express 243 in exponential form, we factorise it into prime factors:

• 243 ÷ 3 = 81
• 81 ÷ 3 = 27
• 27 ÷ 3 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Thus, we find that:

243 = 3⁵, so the correct answer is option A.

32 can be expressed as:

• 2 × 2 × 2 × 2 × 2

This can also be written in exponential form as:

2⁵

Therefore, the exponential form of 32 is 2⁵.

To express 125 in its exponential form, we factorise it into prime factors:

• 125 ÷ 5 = 25
• 25 ÷ 5 = 5
• 5 ÷ 5 = 1

Thus, 125 can be written as:

5 × 5 × 5, which is 5³.

Therefore, the correct answer is B.

81 can be expressed as 3 multiplied by itself four times, which is written as 3⁴.