Laws of Indices

Multiplication & Division

100

Express the product of 2⁴ x 2³ in index form.

2⁷

200

Express the quotient of p⁵q³r⁴ / p³q²r in index form.

p²qr³

300

Determine the value of 3⁴ x 3^-5 x 3².

3

400

What  is 3a⁵ x 4a² / 2a³ ?

6a⁴

500

Simplify completety: (2x^-2y³)² (4x³y^-1) / 8x^-1y²

2x⁰y³ = 2y³

Power of a Power & Product of a Power

100

Simplify (x³)⁴

x¹²

200

Simplify (3a²)²

9a⁴

300

Simplify (x²)³ (x⁴)²

x¹⁴

400

A student says: (3x²)⁴ = 3x⁸. IS the student correct? Explain.

No. The exponent must apply to both the coefficient and variable.

500

Simplify (x^-2y³)⁴

y¹²/x⁸

Power of a Quotient

100

Simplify (2/5)³

8/125

200

Simplify (3/5)^-2

25/9

300

Simplify (2x²/3y)^-3

27y³ / 8x⁶

400

A student writes: (2/3)^-2 = -4/9. What is the student's error and what is the correct answer?

A negative exponent does not make the answer negative. It means take the reciprocal (flip).

(2/3)^-2 = (3/2)² = 9/4

500

Without using calculator, simplify (2x³/5y²)^-2 (5y/2x)²

625y⁶/16x⁸

Zero & Negative Power

100

Evaluate 7⁰

1

200

Simplify x⁰ + y⁰

2 

300

Simplify 5^-3

1/125

400

Simplify (2x^-2)⁰ / y^-3

y³

500

Simplify a-³b² / c^-2

b²c² / a³

Fractional Power

100

Evaluate 16^1/2

4

200

Evaluate 27^1/3

3

300

What is the value of 27^2/3?

9

400

Simplify p^1/2 x p^3/2

p²

500

Simplify completely: 16^3/4 / 8^2/3

2