Exponent Quiz - Level 1

(4x⁵)³

(4x⁵)³ = 4x⁵ * 4x⁵ * 4x⁵ = 64x¹⁵ Again, you can expand the problem in order to solve it (as above), or you could raise every term inside the parentheses to the 3rd power, so 4³ = 64 and (x⁵)³ = x¹⁵

(x⁵)⁶

(x⁵)⁶ = x⁵ * x⁵ * x⁵ * x⁵ * x⁵ * x⁵ = x³⁰ You can expand the problem in order to solve it (as above), or you could raise x⁵ to the 6th power by multiplying the exponents. 5*6 = 30, which becomes the new exponent.

Rewrite the problem below as 2 to the power of an exponent. 2 * 2 * 2 * 2 * 2 * 2 * 2

2 * 2 * 2 * 2 * 2 * 2 * 2 = 2⁷

(2x⁴)⁴

2x⁴ * 2x⁴ * 2x⁴ * 2x⁴ = 16x¹⁶

2x⁴ⁿ⁻² * 3x⁷ⁿ⁺⁹

2x⁴ⁿ⁻² * 3x⁷ⁿ⁺⁹ = 6x¹¹ⁿ⁺⁷

2x⁹ * 3x²

2x⁹ * 3x² = 6x¹¹

2⁴ * 2⁸

2¹²

2⁵ * 2³ * 2⁴

2⁵ * 2³ * 2⁴ = 2¹²

(3x²)³

3x² * 3x² * 3x² = 27x⁶ You can expand the problem in order to solve it (as above), or you could raise every term inside the parentheses to the 3rd power, so 3³ = 27 and (x²)³ = x⁶

4x⁶ * 6x⁸

4x⁶ * 6x⁸ = 24x¹⁴

7 * 7⁻² * 7

7⁰ = 1 Remember that if a term doesn't have an exponent, the implied exponent is 1. So 7 = 7¹

x * x * x

x³

x³ / x⁻²

x³⁻⁻² = x³⁺² = x⁵

(x⁴)¼

x¹ = x

x⁵ * x²

x⁷

x³ / x⁵

x⁻²

x⁴ / x¹⁰

x⁻⁶ = 1 / x⁶

x / x⁴

x / x⁴ = x¹ / x⁴ = x¹⁻⁴ = x⁻³ = 1/x³

x * x

x²

x⁵ / x³

x²