Laws of Exponents for Real Numbers | Number Systems | Assessment | English | Grade 9

If a is a real number, x and y are integers, then aˣ . aʸ = ?

• aˣʸ

• aˣ⁻ʸ

• (a)ˣ

• aˣ⁺ʸ

Answer explanation

When we multiply same base with different exponents, we add the exponents. aᵐ . aⁿ = aᵐ⁺ⁿ

Tags

CCSS.8.EE.A.1

Simplify 26⁻¹³ / 26¹¹ = ?

• 26⁻²

• 26²

• 26⁻²⁴

• 26²⁴

Answer explanation

We know that aᵐ/aⁿ = aᵐ⁻ⁿ. By applying the same law of exponents for 26⁻¹³ / 26¹¹ We will get 26⁻¹³ / 26¹¹ = 26⁻¹³⁻¹¹ = 26⁻²⁴

Tags

CCSS.8.EE.A.1

Value of 64³ᐟ² is ______

• 512

• 8

• -512

• 262

Answer explanation

64³ᐟ² = (64¹ᐟ²)³ =(√64)³ = (8)³ = 512

Tags

CCSS.HSN.RN.A.2

Value of (21¹ᐟ²)⁴ is _____

• 441

• (21)¹ᐟ² ⁺ ⁴

• 414

• (21)¹ᐟ⁴ ⁻ ²

Answer explanation

We know that (aᵐ)ⁿ = aᵐⁿ Hence, (21¹ᐟ²)⁴ = 21¹ᐟ² ˣ ⁴ = 21⁴ᐟ² = 21² = 441

Tags

CCSS.HSN.RN.A.2

Value of ∜(121)⁻⁴ = ____

• 121

• 1/121

• 120

• 1/11

Answer explanation

∜(121)⁻⁴ = ∜(1/121)⁴ = (1/121)⁴ ˣ ¹ᐟ⁴ = 1/121

216¹ᐟ³ - 216¹ᐟ² = _____

• 6 - √6

• 6 (1 - √6)

• 216¹ᐟ³ ᐨ ¹ᐟ²

• 216¹ᐟ³ ⁺ ¹ᐟ²

Answer explanation

We can't solve 216¹ᐟ³ - 216¹ᐟ² by law of exponents. But we can write 216¹ᐟ³ as ∛216 and 216¹ᐟ² as √216 Hence, 216¹ᐟ³ - 216¹ᐟ² = ∛216 - √216 = 6 - 6√6 = 6 (1 - √6)

(1296)⁰ᐧ¹⁸ × (1296)⁰ᐧ⁰⁷

• 6

• 36

• 26

• 16

Answer explanation

(1296)⁰ᐧ¹⁸ × (1296)⁰ᐧ⁰⁷ = (1296)⁰ᐧ¹⁸ ⁺ ⁰ᐧ⁰⁷ = (1296)⁰ᐧ²⁵ = (1296)¹ᐟ⁴ = (6⁴)¹ᐟ⁴ = 6⁴ ˣ ¹ᐟ⁴ = 6

Tags

CCSS.8.EE.A.1