Review Basic Index Laws (multiplication, division, zero)

What is the correct law for multiplication? a^m x aⁿ =

• a^m+n

• a^m + aⁿ

• a^mxn

• a^mn

Answer explanation

The correct law for multiplication states that a^m x a^n = a^(m+n). This means when multiplying two powers with the same base, you add the exponents. Therefore, the correct answer is a^(m+n).

What is the correct law for division? a^m ÷ aⁿ =

• a^m-n

• a^m - aⁿ

• a^m÷n

• a^m/n

Answer explanation

The law for division states that a^m ÷ a^n = a^(m-n). This means you subtract the exponent of the denominator from the exponent of the numerator, making a^(m-n) the correct choice.

Simplify: b¹⁷ x b⁵

• b²²

• b⁸⁵

• (b²)²²

• b¹²

Answer explanation

To simplify b¹⁷ x b⁵, use the property of exponents that states a^m x aⁿ = a^m+n. Thus, b¹⁷ x b⁵ = b¹⁷⁺⁵ = b²², which is the correct answer.

Simplify: w²⁴ ÷ w⁸

• w¹⁶

• w³

• w³²

• w^24/8

Answer explanation

To simplify w^24 ÷ w^8, subtract the exponents: 24 - 8 = 16. Thus, the result is w^16, which matches the correct answer choice.

Simplify: f⁰

• 1

• f

• f¹

• 0

Answer explanation

The notation f⁰ represents any function raised to the power of zero, which is always equal to 1. Therefore, the correct answer is 1.

Simplify: (3x²y³)⁰

• 1

• 0

• 3

• 3x²y³

Answer explanation

Any expression raised to the power of 0 equals 1, except for 0 itself. Therefore, (3x²y³)⁰ simplifies to 1.

Simplify: 3x³ × 6x⁸

• 18x¹¹

• 18x²⁴

• 9x¹¹

• 9x²⁴

Answer explanation

To simplify 3x^3 × 6x^8, multiply the coefficients (3 × 6 = 18) and add the exponents (3 + 8 = 11). Thus, the result is 18x^11, which matches the correct answer.

Simplify: 42m¹² ÷ 7m⁶

• 6m⁶

• 6m²

• 35m⁶

• 35m²

Answer explanation

To simplify 42m^12 ÷ 7m^6, divide the coefficients: 42 ÷ 7 = 6. For the variables, subtract the exponents: m^(12-6) = m^6. Thus, the result is 6m^6, which matches the correct answer.

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

• 16x⁸y⁹

• 16x²y⁴

• 60x⁸y⁹

• 60x²y⁴

Answer explanation

To simplify, divide coefficients and subtract exponents: (64 ÷ 4) = 16, x^(16-8) = x^8, y^(12-3) = y^9. Thus, the result is 16x^8y^9, matching the correct choice.

What is the correct law for zero exponent? a⁰ =

• a¹

• 1

• a

• 0

Answer explanation

The law for zero exponent states that any non-zero number raised to the power of zero equals 1. Therefore, a⁰ = 1 is the correct answer.