Simplifying Exponential Expressions

True or false: When multiplying expressions with the same base, add the exponents. For example, (2³)(2⁵) = 2³⁺⁵ = 2⁸.

• True 

• False

Answer explanation

When you multiply expressions with the same base, you can combine the exponents by adding them. For example, (2³)(2⁵) = 2³⁺⁵ = 2⁸. If you have a^m × aⁿ, where a is the base, the result is a^m+n.

Tags

CCSS.6.EE.A.1

CCSS.6.EE.A.3

True or false: When dividing expressions with the same base, divide the exponents. For example, 2⁹ ÷ 2³ = 2^9÷3 = 2³.

• True

• False

Answer explanation

So, the statement is false. When you divide expressions with the same base, you subtract the exponents, not divide them. So, the statement is false. For example, 2⁹ ÷ 2³ = 2^9-3 = 2⁶. If you have a^m ÷ aⁿ, where a is the base, the result is a^m-n.

True or false: When taking the power of a power, multiply the exponents. For example, (2³)⁴ = 2^3×4 = 2¹².

• True 

• False

Answer explanation

When you have a power raised to another power, you multiply the exponents. For example, (2³)⁴ = 2^3×4 = 2¹². When you have an expression like am raised to the power of n (written as (a^m)ⁿ, the result is a^m×n.

Tags

CCSS.6.EE.A.1

CCSS.6.EE.A.3

Simplify the expression (c^-7)(c¹¹).

• c¹⁸

• c⁴

• c^-18

• c^-77

Answer explanation

When you multiply expressions with the same base, you add the exponents. In this case, you have c^-7 × c¹¹, so you add the exponents: c^-7 × c¹¹ = c^-7+11 = c⁴.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the expression z¹⁵ / z⁸.

• z²³ 

• z^-7 

• z^15/8

• z⁷

Answer explanation

When you divide expressions with the same base, you subtract the exponents. In this case, you have z¹⁵ / z⁸, so you subtract the exponents: z¹⁵ / z⁸ = z^15-8 = z⁷.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the expression (k³)⁶.

• k¹⁸

• k⁹ 

• k²⁴

• k^-2

Answer explanation

When you raise a power to another power, you multiply the exponents. In this case, you have (k³)⁶, so you multiply the exponents: (k³)⁶ = k^3×6 = k¹⁸.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the expression (2a^-9)(11a¹⁴).

• 22/a⁵

• 22a^-23

• 22a⁵

• 22a²³

Answer explanation

When you multiply expressions with the same base, you add the exponents. In this case, you have (2a^-9)(11a¹⁴), so you multiply the coefficients and add the exponents: (2a^-9)(11a¹⁴) = 22a^-9+14 = 22a⁵.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Simplify the expression (3^-2)^-4.

• 3⁶

• 3⁸

• 3^-2

• 3²⁴

Answer explanation

When you raise a power to another power, you multiply the exponents. In this case, you have (3^-2)^-4, so you multiply the exponents: (3^-2)^-4 = 3^(-2)×(-4) = 3⁸.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the expression (4⁹ × 6¹⁷) / (4^-2 × 6⁸).

• 4⁷ × 6⁹

• 4¹¹ × 6^-9

• 4⁷ × 6^-9

• 4¹¹ × 6⁹

Answer explanation

When dividing expressions with the same base, you subtract the exponents. In this case, you have (4⁹ × 6¹⁷) / (4^-2 × 6⁸), so you subtract the exponents: (4⁹ × 6¹⁷) / (4^-2 × 6⁸) = 4^9-(-2) × 6^17-8 = 4¹¹ × 6⁹.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the expression (15 × 8⁵)⁶.

• 15⁶ × 8³⁰

• 120¹¹

• 15 × 8¹¹

• 120³⁰

Answer explanation

When you raise a power to another power, you multiply the exponents. In this case, you have (15 × 8⁵)⁶, so you multiply the exponents: (15 × 8⁵)⁶ = (15¹ × 8⁵)⁶ = 15^1×6 × 8^5×6 = 15⁶ × 8³⁰.

Tags

CCSS.HSN.RN.A.2