exponents

The value of 2^-2 is:

• 4

• 1/4

• 1/2

• 2

Answer explanation

To find 2^-2, we use the rule that a negative exponent means the reciprocal. Thus, 2^-2 = 1/(2^2) = 1/4. Therefore, the correct answer is 1/4.

2² x 2³ x 2⁴ is equal to

• 2²⁴

• 2⁵

• 2⁹

• 2^-9

Answer explanation

To solve 2² x 2³ x 2⁴, add the exponents: 2 + 3 + 4 = 9. Thus, 2² x 2³ x 2⁴ = 2⁹, making the correct answer 2⁹.

If (–3)^m+1 × (–3)⁵ = (–3)⁷, then the value of m is:

• 5

• 1

• 7

• 3

Answer explanation

To solve for m, use the property of exponents: (–3)^(m+1+5) = (–3)^7. This simplifies to m + 6 = 7. Solving for m gives m = 1. Thus, the correct answer is 1.

What is the value of (2² + 3² + 4²)⁰?

• 0

• 41

• 9

• 1

Answer explanation

Any non-zero number raised to the power of 0 equals 1. Here, (2^2 + 3^2 + 4^2) evaluates to 29, which is non-zero. Therefore, (2^2 + 3^2 + 4^2)^0 = 1.

What is the value of 2³ x 2² x 2^-1?

• 2⁴

• 2⁵

• 2²

• 2³

Answer explanation

To solve 2^3 x 2^2 x 2^-1, use the property of exponents: a^m x a^n = a^(m+n). Here, 3 + 2 - 1 = 4. Thus, the expression simplifies to 2^4, which is the correct answer.

Calculate the value of (5⁰ + 2⁰)².

• 25

• 4

• 1

• 0

Answer explanation

To solve (5^0 + 2^0)^2, first calculate 5^0 = 1 and 2^0 = 1. Thus, (1 + 1)^2 = 2^2 = 4. The correct answer is 4.

The value of 3^-3 is:

• 1/27

• 3

• 27

• 1/9

Answer explanation

To find 3^-3, we calculate 1/(3^3). Since 3^3 = 27, we have 1/27. Therefore, the value of 3^-3 is 1/27, which is the correct answer.

700000000 is equal to:

• 7 × 10⁸

• 7 × 10⁹

• 7 × 10⁷

• 7 × 10⁶

Answer explanation

700000000 can be expressed in scientific notation as 7 × 10^8. This is because 700000000 is 7 followed by 8 zeros, which corresponds to the exponent of 10 being 8. Thus, the correct answer is 7 × 10⁸.

1.8 × 10¹¹ is equal to

• 18000000000

• 180000000000

• 1800000000000

• 1800000000

Answer explanation

1.8 × 10^11 means 1.8 multiplied by 10 raised to the power of 11. This equals 1.8 followed by 11 zeros, which is 180000000000. Thus, the correct answer is 180000000000.

865000 is equal to

• 8.65 × 10⁵

• 8.65 × 10⁴

• 8.65 × 10⁶

• 8.65 × 10⁰

Answer explanation

To express 865000 in scientific notation, we move the decimal point 5 places to the left, resulting in 8.65. Thus, 865000 = 8.65 × 10^5, making the correct choice 8.65 × 10⁵.