Laws of Exponents

Simplify: x³ • x⁵

• x⁸

• x¹⁵

• x²

• x⁸/x⁵

Answer explanation

When multiplying terms with the same base, add the exponents.

Simplify: (y²)⁴

• y⁶

• y⁸

• 2y²

• y²⁴

Answer explanation

When raising a power to a power, multiply the exponents.

Simplify: a⁵ / a²

• a⁷

• a³

• a²/a⁵

• a¹⁰

Answer explanation

When dividing terms with the same base, subtract the exponents.

Simplify: (2m²)³

• 6m⁶

• 2m⁶

• 8m⁶

• 8m⁵

Answer explanation

Remember to cube both the coefficient (2) and the variable (m²).

Simplify: (x⁻²)³

• x⁻⁶

• x⁶

• x⁻⁵

• 1/x⁶

Answer explanation

Remember the rule for raising a power to a power.

Simplify: 5x⁻³

• 5/x³

• -15x

• 5x³

• 1/5x³

Answer explanation

A negative exponent indicates the reciprocal.

Simplify: (4a²b) / (2ab)

• 2a

• 2a²

• 2b

• 2ab

Answer explanation

Simplify the coefficients and subtract the exponents of the variables.

Simplify: (mⁿ)⁵

• 5mⁿ

• mⁿ⁺⁵

• m⁵ⁿ

• mⁿ⁻⁵

Answer explanation

Remember the rule for raising a power to a power.

Simplify: (p³/q²)⁻¹

• p³/q²

• q²/p³

• -p³/q²

• p⁻³/q⁻²

Answer explanation

When raising a fraction to a negative power, invert the fraction and change the exponent to positive.

True/False: x⁰ = 0

• True

• False

Answer explanation

Any non-zero base raised to the power of zero equals 1.