Laws of Indices

Laws of indices and its applications

Quiz Type

Practice

Subject

Mathematics

Level

Senior High School

Questions

10 questions

Created By

Kwabena Appiagyei

Quick Rules

Time limit: 50 minutes
Multiple attempts are not allowed
All questions must be answered to submit

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Question 1 of 10

Question 1

Basic multiple choice Remembering

What is the law of indices that states any non-zero number raised to the power of zero equals one?

A number raised to the power of one

A number raised to the power of zero

Correct

A number raised to the power of negative one

A number raised to the power of itself

Explanation

According to the law of indices, any non-zero number raised to the power of zero is equal to one.

Question 2

Basic multiple choice Understanding

Which of the following represents the product of two powers with the same base according to the laws of indices?

Add the exponents

Correct

Subtract the exponents

Multiply the exponents

Divide the exponents

Explanation

When multiplying two powers with the same base, you add the exponents together.

Question 3

Basic multiple choice Understanding

According to the laws of indices, what is the result of raising a power to another power?

Multiply the exponents

Correct

Add the exponents

Subtract the exponents

Leave the exponents unchanged

Explanation

When raising a power to another power, you multiply the exponents according to the laws of indices.

Question 4

Basic multiple choice Remembering

What is 2^3 multiplied by 2^2 according to the laws of indices?

2^6

2^1

2^0

2^5

Correct

Explanation

Using the law of indices, you add the exponents: 3 + 2 = 5, thus 2^3 * 2^2 = 2^5.

Question 5

Basic multiple choice Understanding

What happens when you divide two powers with the same base according to the laws of indices?

Add the exponents

Subtract the exponents

Correct

Multiply the exponents

Change the base

Explanation

When dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.

Question 6

Complex multiple choice Understanding

If a company decides to introduce a new product and its projected sales increase by a factor of 3^2 in its first year, what will be the relationship of this sales increase to its initial sales, assuming initial sales are represented as 'S'? Which of the following expressions represents the new sales figure after one year?

S * 9

Correct

S * 6

S + 9

S^2 * 3

Explanation

The correct answer is S * 9 because an increase by a factor of 3^2 means multiplying the initial sales by 9 (the square of 3). Options B, C, and D are misconceived interpretations of the factor increase, as they suggest either incorrect multiplication or addition of sales figures.

Question 7

Complex multiple choice Understanding

A student needs to simplify the expression (x^3 * y^2) / (x^2 * y^5). Which of the following simplified forms correctly applies the laws of indices?

x^(3-2) * y^(2-5)

Correct

x^(3+2) * y^(5-2)

x^(3/2) * y^(2-5)

x^(3-5) * y^(2-2)

Explanation

The correct simplification is x^(3-2) * y^(2-5), which correctly applies the law of indices for division where exponents of the same base are subtracted. The other options either incorrectly add exponents or misapply the laws, leading to incorrect results.

Question 8

Case based multiple choice Understanding

[Case Scenario] In a mathematics class, students are being introduced to the laws of indices. One student, Alice, presents the expression 2^3 * 2^4 to her classmates and claims that it can be simplified using the laws of indices. She insists that since the bases are the same (2), she can add the exponents. After some discussion, the teacher asks the class to evaluate Alice's claim. Question: What is the correct simplification of the expression 2^3 * 2^4 using the laws of indices?

2^7

Correct

2^12

2^1

Explanation

Alice correctly applied the laws of indices by adding the exponents of the same base. Thus, 2^3 * 2^4 simplifies to 2^(3+4) = 2^7.

Question 9

Case based multiple choice Understanding

[Case Scenario] During a science experiment, Ben needs to express the relationship between pressure and volume in terms of gas laws. He finds the equation PV^n = K, where P is pressure, V is volume, and K is a constant. To rewrite this relationship using the laws of indices, he considers raising both sides of the equation to the power of 1/n. After this, he wants to express V in terms of P. Question: What is the correct expression for V in terms of P after applying the laws of indices to the equation?

V = K^(1/n) / P^(1/n)

Correct

V = P^(n/K)

V = K * n / P

V = P^n / K

Explanation

By applying the laws of indices correctly, Ben can isolate V by manipulating the equation and rewriting it as V = (K/P)^(1/n). This demonstrates the application of exponent laws effectively.

Question 10

Case based multiple choice Understanding

[Case Scenario] In her homework, Clara is tasked to simplify expressions using the laws of indices. She encounters the expression (3^4 / 3^2) and approaches it with the intention of applying the rules of exponents. She is aware that when dividing powers with the same base, she can subtract the exponents. However, she is unsure about how this applies when both exponents are negative. Her expression has also been translated into 3^(-2) / 3^(-4) during the process, which puzzles her. Question: What is Clara's correct simplification of the expression 3^4 / 3^2?

3^2

Correct

3^-2

3^6

3^0

Explanation

Clara correctly simplified 3^4 / 3^2 to 3^(4-2) = 3^2. It demonstrates an understanding of the laws of indices in handling division of like bases.