Operations of Monomials

Simplify.

(3x⁴y⁵)²

• 9x⁸y¹⁰

• 6x⁸y¹⁰

• 3x⁸y¹⁰

• x⁸y¹⁰

Answer explanation

To simplify the expression (3x^4y^5)^2, we raise each term inside the parentheses to the power of 2. This gives us 9x^8y^10, which is the correct choice.

Simplify.

• -9a³

• -9a⁶

• -24a⁶

• 30a⁶

Answer explanation

The correct answer is -9a^6 because it is the only choice with a negative sign and the highest exponent of a.

Simplify.

• -4x²y

• 4x²y

• -4x⁸y³

• -4x³y²

Answer explanation

The correct choice is -4x^2y because it is the only option that matches the given expression.

Simplify.

• -5x⁴y³

• 5x⁴y³

• 5x¹⁰y⁷

• -5x¹⁰y⁷

Answer explanation

The correct answer is 5x^4y^3 because it is the only choice that matches the given expression.

-20x⁶ + (-10x⁶)

• 10x¹²

• -30x⁶

• -10x⁶

• -30x¹²

Answer explanation

To subtract the terms, combine the coefficients. -20x^6 + (-10x^6) = -30x^6. Therefore, the correct answer is -30x^6.

Simplify the following monomial: -5a^2b^{2\ }-\ a^2b^2

Answer explanation

To simplify the monomial, combine like terms. The correct choice is -6a^2b^2 because the exponents are added when multiplying like bases.

Find the sum of 16y² and -5y².

• -11y²

• 21y²

• 11y²

• 16y² - 5y²

Answer explanation

The sum of 16y^2 and -5y^2 is 11y^2, which is the correct choice.

Subtract 9a from -15a.

• -6a

• -24a

• 24a

• 6a

Answer explanation

To subtract 9a from -15a, we subtract the coefficients: -15 - (-9) = -15 + 9 = -6. The answer is -6a.

• 2a²b⁶
• 1/2a²b⁶
• b⁶/2a²
• 2b⁶/a²

Evaluate the expression using the quotient rule.

• x¹³

• x⁵

• x³⁶

• x^-5