Question

Simplify the expression to a form in which 2 is raised to a single integer power. (2¹⁰)³ 2⁻¹⁰/(2⁻⁷)

Answer 1

To simplify the expression (2¹⁰)³ 2⁻¹⁰/(2⁻⁷), multiply the exponents inside the parentheses and subtract the exponents outside the parentheses. The simplified form is 2²⁷.

Step-by-step explanation:

To simplify the expression (2¹⁰)³ 2⁻¹⁰/(2⁻⁷), we need to apply the rules of exponents. First, we can simplify the expression inside the parentheses by multiplying the exponents: (2¹⁰)³ = 2¹⁰ × 3 = 2³⁰. Next, we can simplify the expression outside the parentheses by subtracting the exponents: 2⁻¹⁰/(2⁻⁷) = 2⁻¹⁰-(-7) = 2⁻³.

Combining these simplifications, we have 2³⁰ × 2⁻³. Applying the rule of multiplying exponentiated quantities, we add the exponents: 2³⁰ × 2⁻³ = 2³⁰+(-3) = 2²⁷.