Cuestionario: Mastering Indices and Exponential Expressions — 5 preguntas

1. How does an index differ from a base number in the context of powers?

A. The index indicates how many times the base is multiplied by itself, while the base is the number being raised to a power.

B. The index is the number being raised to a power, while the base indicates how many times it is multiplied.

C. The index and base are interchangeable terms for the same concept.

D. The index is the result of raising the base to a power.

Answer: (A)

Explicación

The index indicates how many times the base is multiplied by itself, and the base is the number being raised to a power, as supported by the source excerpt.

2. What does an index (or exponent) indicate in an expression involving indices?

A. The number being raised to a power

B. The result of the multiplication

C. The value of the base number

D. The number of times the base number is multiplied by itself

Answer: (D)

Explicación

The source states that an index (or exponent) indicates the number of times the base number is multiplied by itself.

3. Which statement matches the topic "Laws of indices and their application"?

A. Base Number : the number being raised to a power in an expression involving indices

B. An index (or exponent) indicates the number of times the base number is multiplied by itself. It acts as a shorthand notation, simplifying repeated multiplication. The base number is the…

C. Index (Exponent) : a numerical indicator that shows how many times the base number is multiplied by itself

D. Product Law of Indices : a rule that states when multiplying two exponential expressions with the same base, the exponents are added together. For example, a^m × a^n = a^(m + n)

Answer: (D)

Explicación

This statement comes directly from the course section dedicated to this topic: Product Law of Indices : a rule that states when multiplying two exponential expressions with the same base, the exponents are added together. For example, a^m × a^n = a^(m + n).

4. What is the Quotient Law of Indices?

A. Any base raised to the zero power equals zero.

B. When multiplying two exponential expressions with the same base, add their exponents.

C. When raising a power to another power, multiply the exponents.

D. When dividing two exponential expressions with the same base, subtract the exponents.

Answer: (D)

Explicación

The Quotient Law of Indices states that when dividing two exponential expressions with the same base, the exponents are subtracted, as supported by the source.

5. What is the purpose of applying laws of indices when simplifying exponential expressions?

A. To change the base of an expression to any arbitrary number

B. To make the expression more complex for advanced calculations

C. To eliminate variables from the expression

D. To combine powers with the same base by adding or subtracting exponents

Answer: (D)

Explicación

Applying laws of indices allows combining powers with the same base by adding or subtracting exponents, which simplifies the expression.