Exponent Rules

Question 1

What is the product rule for exponents? / Quelle est la règle du produit pour les exposants ?

Answer 1

Add the exponents when multiplying powers with the same base / Additionner les exposants quand on multiplie des puissances avec la même base

Question 2

Simplify: 2³ × 2⁴ / Calcule: 2³ × 2⁴

Answer 2

2⁷ = 128 / 2⁷ = 128

Question 3

Simplify: x² × x⁵ / Calcule: x² × x⁵

Answer 3

x⁷ / x⁷

Question 4

What is the quotient rule for exponents? / Quelle est la règle du quotient pour les exposants ?

Answer 4

Subtract the exponents when dividing powers with the same base / Soustraire les exposants quand on divise des puissances avec la même base

Question 5

Simplify: 5⁶ ÷ 5² / Calcule: 5⁶ ÷ 5²

Answer 5

5⁴ = 625 / 5⁴ = 625

Question 6

Simplify: y⁷ ÷ y³ / Calcule: y⁷ ÷ y³

Answer 6

y⁴ / y⁴

Question 7

What is the power of a power rule? / Quelle est la règle de la puissance d’une puissance ?

Answer 7

Multiply the exponents / Multiplier les exposants

Question 8

Simplify: (3²)³ / Calcule: (3²)³

Answer 8

3⁶ = 729 / 3⁶ = 729

Question 9

Simplify: (x³)² / Calcule: (x³)²

Answer 9

x⁶ / x⁶

Question 10

What is the power of a product rule? / Quelle est la règle de la puissance d’un produit ?

Answer 10

Distribute the exponent to each factor / Distribuer l’exposant à chaque facteur

Question 11

Simplify: (2x)³ / Calcule: (2x)³

Answer 11

2³x³ = 8x³ / 2³x³ = 8x³

Question 12

Simplify: (ab)² / Calcule: (ab)²

Answer 12

a²b² / a²b²

Question 13

What does a negative exponent mean? / Que signifie un exposant négatif ?

Answer 13

It means take the reciprocal of the base and make the exponent positive / Cela signifie prendre l’inverse de la base et rendre l’exposant positif

Question 14

Simplify: 2⁻³ / Calcule: 2⁻³

Answer 14

1 ÷ 2³ = 1/8 / 1 ÷ 2³ = 1/8

Question 15

Simplify: x⁻² / Calcule: x⁻²

Answer 15

1 ÷ x² / 1 ÷ x²

Question 16

Simplify: (3x⁻¹)² / Calcule: (3x⁻¹)²

Answer 16

9x⁻² = 9 ÷ x² / 9x⁻² = 9 ÷ x²

Question 17

What is the zero exponent rule? / Quelle est la règle de l’exposant zéro ?

Answer 17

Any non-zero base to the power of zero equals 1 / Toute base non nulle à la puissance zéro est égale à 1

Question 18

Simplify: 7⁰ / Calcule: 7⁰

Answer 18

1 / 1

Question 19

Simplify: (x + 5)⁰ / Calcule: (x + 5)⁰

Answer 19

1 (as long as x + 5 ≠ 0) / 1 (tant que x + 5 ≠ 0)

Question 20

Simplify: x³ ÷ x³ / Calcule: x³ ÷ x³

Answer 20

x⁰ = 1 / x⁰ = 1

Question 21

Which is done first, power of a power or multiplication? / Qu’est-ce qu’on fait en premier, puissance d’une puissance ou multiplication ?

Answer 21

Power of a power first / La puissance d’une puissance d’abord

Question 22

Simplify: (2³)² × 2 / Calcule: (2³)² × 2

Answer 22

2⁶ × 2 = 2⁷ = 128 / 2⁶ × 2 = 2⁷ = 128

Question 23

Where do we see exponents in real life?

Answer 23

In area/volume, scientific notation, population growth, compound interest, and computer science.

Question 24

Word Problem: The side of a square is 5 cm. Find its area.

Answer 24

A = 5² = 25 cm².

Question 25

Word Problem: The side of a cube is 3 m. Find its volume.

Answer 25

V = 3³ = 27 m³.

Question 26

Word Problem: A bacteria population doubles every hour. Start with 1 bacterium. How many after 4 hours?

Answer 26

1 × 2⁴ = 16 bacteria.

Question 27

Word Problem: A population triples every day for 3 days. Starting with 5, what is the population?

Answer 27

5 × 3³ = 5 × 27 = 135.

Question 28

Word Problem: Write 300 000 in scientific notation.

Answer 28

3 × 10⁵.

Question 29

Word Problem: Write 0.004 in scientific notation.

Answer 29

4 × 10⁻³.

Question 30

Why is 10⁶ called 'a million'?

Answer 30

Because it is 1 followed by 6 zeros.

Question 31

Word Problem: Simplify (10³)(10⁴) to write population growth in scientific notation.

Answer 31

10³⁺⁴ = 10⁷.

Question 32

Word Problem: Simplify (10⁵) ÷ (10²) to show population decrease.

Answer 32

10³.

Question 33

Word Problem: The area of a square is x². If x = 7, what is the area?

Answer 33

7² = 49.

Question 34

Word Problem: The volume of a cube is x³. If x = -2, what is the volume?

Answer 34

(-2)³ = -8.

Question 35

Word Problem: A scientist writes the mass of an atom as 3 × 10⁻²³ g. What does this mean?

Answer 35

It is a very small number: 0.00000000000000000000003 g.

Question 36

Why are exponents useful in science?

Answer 36

They make very big or very small numbers easier to write and compare.

Question 37

Why are exponents important in algebra?

Answer 37

They let us describe repeated multiplication and growth patterns efficiently.