Exponent Properties Review (Math Masters)

What is the value of 2³×2⁴?

• 2⁶

• 2⁵

• 2⁸

• 2⁷

Answer explanation

To solve 2^3 × 2^4, use the property of exponents: a^m × a^n = a^(m+n). Here, 3 + 4 = 7, so 2^3 × 2^4 = 2^7. Thus, the correct answer is 2^7.

What is the value of (3²)³?

• 9

• 3³

• 3⁵

• 3⁶

Answer explanation

To solve (3^2)^3, use the power of a power rule: multiply the exponents. Thus, (3^2)^3 = 3^(2*3) = 3^6. Therefore, the correct answer is 3^6.

Simplify x⁵÷x².

• x¹

• x⁴

• x²

• x³

Answer explanation

To simplify x^5 ÷ x^2, subtract the exponents: 5 - 2 = 3. Thus, x^5 ÷ x^2 = x^3. The correct answer is x^3.

What is the value of 5⁰?

• 5

• 10

• 0

• 1

Answer explanation

Any non-zero number raised to the power of 0 equals 1. Therefore, 5⁰ = 1.

Which of the following represents the property of exponents that states a^m×aⁿ=a^m+n?

• Product of Powers Property

• Zero Exponent Property

• Quotient of Powers Property

• Power of a Product Property

Answer explanation

The property a^m × a^n = a^(m+n) is known as the Product of Powers Property. It states that when multiplying two powers with the same base, you add their exponents.

Simplify a⁶/a².

• a³

• a⁴

• a²

• a⁸

Answer explanation

To simplify a^6/a^2, subtract the exponents: 6 - 2 = 4. Thus, a^6/a^2 = a^4. The correct answer is a^4.

What is the result of (2xy³)²?

• 8x⁴y⁹

• 4x²y⁶

• 2x³y⁶

• 4xy³

Answer explanation

To simplify (2xy^3)^2, apply the power of a product rule: (a*b)^n = a^n * b^n. Thus, (2^2)(x^2)(y^{3*2}) = 4x^2y^6. The correct answer is 4x^2y^6.

What does 7^-2 equal?

• 1/53

• 1/49

• 7

• 1/10

Answer explanation

To solve 7^-2, use the property of exponents: a^-n = 1/aⁿ. Thus, 7^-2 = 1/7² = 1/49. Therefore, the correct answer is 1/49.

Which expression is equivalent to x⁴⋅x³⋅x²?

• x⁶

• x⁷

• x⁸

• x⁹

Answer explanation

To combine the expressions, add the exponents: 4 + 3 + 2 = 9. Therefore, x^4 ⋅ x^3 ⋅ x^2 = x^9, making x^9 the correct answer.

Simplify b⁵/b³⋅b².

• b¹

• b⁵

• b⁰

• b³

Answer explanation

To simplify b^5/b^3⋅b^2, first apply the quotient rule: b^(5-3) = b^2. Then, multiply by b^2: b^2⋅b^2 = b^(2+2) = b^4. The correct answer is b^0, which equals 1, indicating no variable remains.