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Olympiad Test: Exponents And Powers - CAT MCQ


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20 Questions MCQ Test - Olympiad Test: Exponents And Powers

Olympiad Test: Exponents And Powers for CAT 2024 is part of CAT preparation. The Olympiad Test: Exponents And Powers questions and answers have been prepared according to the CAT exam syllabus.The Olympiad Test: Exponents And Powers MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Exponents And Powers below.
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Olympiad Test: Exponents And Powers - Question 1

What is the value of (30−40) × 5−3 ?

Detailed Solution for Olympiad Test: Exponents And Powers - Question 1

Since ao = 1 for any 'a', (30−40) × 5−3 = (1−1) × 5−3 = 0x5-3=0
as 0xanything=0

Olympiad Test: Exponents And Powers - Question 2

Expand 1256.249 using exponents.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 2

⇒ (1 x 1000) +(2 x 100) + (5 x 10) + (6 x 1) + (2/10) + (4/100) + (9/1000) .

⇒ (1 x 103) + (2 x 102) + (5 x 101) + (6 x 100) + (2 x 10-1) + (4 x 10-2) +(9 x 10-3) (Ans) 

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Olympiad Test: Exponents And Powers - Question 3

What is the solution of 

Detailed Solution for Olympiad Test: Exponents And Powers - Question 3

 33x−5 = 3−2x ⇒ 3x−5 =−2x

[When bases are equal, powers can be equated.] 

⇒ 5x = 5

⇒ x = 1

Olympiad Test: Exponents And Powers - Question 4

Simplify: (−3)2×(5/3)2 

Detailed Solution for Olympiad Test: Exponents And Powers - Question 4

(-3)x (5/3)= (-1)2(3)2-2(25) = 25

Olympiad Test: Exponents And Powers - Question 5

Write the expression using exponents: 89 × 89 × 89 × 89

Detailed Solution for Olympiad Test: Exponents And Powers - Question 5

To write the expression using exponents, we can rewrite the given expression as:
89 × 89 × 89 × 89
Now, let's simplify this expression using exponents:
89 × 89 × 89 × 89 = 89^4
Therefore, the expression 89 × 89 × 89 × 89 can be written as 89^4.
So, the correct answer is option A: 89^4.
Olympiad Test: Exponents And Powers - Question 6

Evaluate exponential expression − 25.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 6

To evaluate the exponential expression -2^5, we need to follow the order of operations, which states that we should perform any exponentiation before any other operations.
1. Start by evaluating the exponent, which is 5.
2. Raise -2 to the power of 5, which means multiplying -2 by itself 5 times.
-2^5 = -2 * -2 * -2 * -2 * -2
= -32
3. The value of the expression -2^5 is -32.
Therefore, the correct answer is B. -32.
Olympiad Test: Exponents And Powers - Question 7

The value of 23 is _____.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 7

23 = 2x2x2 = 8

Olympiad Test: Exponents And Powers - Question 8

Simplify and write in exponential form: p3×p−10

Detailed Solution for Olympiad Test: Exponents And Powers - Question 8

We can simplify the given expression by applying the rule of exponents, which states that when multiplying two powers with the same base, we add their exponents.
1. The given expression is p^3 * p^(-10).
2. According to the rule of exponents, we add the exponents: 3 + (-10) = -7.
3. Therefore, the simplified expression is p^(-7).
4. In exponential form, a negative exponent indicates the reciprocal of the base. So p^(-7) can be written as 1/p^7.
5. Therefore, the simplified and exponential form of the given expression is p^(-7) or 1/p^7.
Hence, the correct answer is A: p^(-7).
Olympiad Test: Exponents And Powers - Question 9

Very small numbers can be expressed in standard form using __________ exponents.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 9

To express very small numbers in standard form, we use negative exponents. Here's a detailed explanation:
1. Standard Form:
- Standard form, also known as scientific notation, is a way to represent very large or very small numbers in a concise and readable format.
- In standard form, a number is expressed as a product of a coefficient and a power of 10.
2. Negative Exponents:
- Negative exponents indicate the reciprocal or multiplicative inverse of a number.
- When we have a very small number, it can be expressed in the form of a fraction with a positive exponent in the denominator.
- However, in standard form, we want the exponent to be positive. So, we use negative exponents to represent the reciprocal of the fraction.
3. Example:
- Let's say we have the number 0.000036.
- To express this number in standard form, we move the decimal point to the right until we have a number between 1 and 10.
- In this case, we move the decimal point 5 places to the right, which gives us 3.6.
- The original number can then be written as 3.6 x 10^(-5), where -5 is the negative exponent representing the number of decimal places the decimal point was moved.
Therefore, very small numbers can be expressed in standard form using negative exponents.
Olympiad Test: Exponents And Powers - Question 10

a= _______

Detailed Solution for Olympiad Test: Exponents And Powers - Question 10

To find the value of a0, we need to understand the basic rule of exponentiation.
Rule: Any number raised to the power of 0 is equal to 1.
Therefore, a0 = 1.
Answer: B: 1.
Olympiad Test: Exponents And Powers - Question 11

The area of a square is given by the formula A = c2. What will be the total area of 5 such similar squares, if the side of a square is 8 ft? 

Detailed Solution for Olympiad Test: Exponents And Powers - Question 11
We have,length of each side of a square, s = 8 ftarea of 1 square = s^2 = 8 x 8 = 64 ft^2Now, area of 5 squares = 5 x 64 = 320 ft^2
Olympiad Test: Exponents And Powers - Question 12

Evaluate the exponential expression (−n)4× (−n)2, for n = 5.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 12
(-n)^4×(-n)^2for n =(-5)^4×(-5)^2 by formula if(a)^n×(a)^m=a^m+n =(-5)^4+2 =-5^6 =5×5×5×5×5×5 =15625
Olympiad Test: Exponents And Powers - Question 13

The area of a square is given by the formula A = side2. What will be the total area of 5such similar squares, if the side of a square is 7 in? 

Detailed Solution for Olympiad Test: Exponents And Powers - Question 13

Side of the square is 7 inches
So area of one square is  7= 49
Total area of 5 such squares is
49×549×5 = 245 in2

Olympiad Test: Exponents And Powers - Question 14

Which of the following is the value of (4 / 5)-9 / (4 / 5)-9?

Detailed Solution for Olympiad Test: Exponents And Powers - Question 14

Olympiad Test: Exponents And Powers - Question 15

Simplify: 25÷ 2−6

Detailed Solution for Olympiad Test: Exponents And Powers - Question 15

25/2-6 = 25-(-6) = 211

Olympiad Test: Exponents And Powers - Question 16

Simplify:  ((1/3)-2 - (1/2)-3)/ (1/4)-2

Detailed Solution for Olympiad Test: Exponents And Powers - Question 16

To simplify the given expression:


((1/3)-2 - (1/2)-3) / (1/4)-2


We can start by simplifying the exponents:


(3/1)2 - (2/1)3 / (4/1)2


Next, we can simplify the numerator and denominator separately:


(9/1) - (8/1) / (16/1)


Now, we can subtract the fractions:


(9 - 8) / 16


Finally, we can simplify the expression:


1/16


Answer: C. 1/16

Olympiad Test: Exponents And Powers - Question 17

Find the value of 

Detailed Solution for Olympiad Test: Exponents And Powers - Question 17

= [(-2/3 )-2 ]1

= (-2/3)-2
= [1 /  (-2/3)]2

= 9/4

Olympiad Test: Exponents And Powers - Question 18

Find the value of the expression a2 for a = 10.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 18

a = 10, a2 = 102
10x10 =100

Olympiad Test: Exponents And Powers - Question 19

Evaluate: - 73

Detailed Solution for Olympiad Test: Exponents And Powers - Question 19

To evaluate -7^3, we need to follow the order of operations, which states that we should perform the exponentiation before the negation.
Steps:
1. Evaluate the exponent: -7^3 = -(7^3).
2. Calculate 7^3: 7^3 = 7 × 7 × 7 = 343.
3. Apply the negation: -(7^3) = -343.
Therefore, the correct answer is A: -343.
Olympiad Test: Exponents And Powers - Question 20

Find the multiplicative inverse of 7−2.

Detailed Solution for Olympiad Test: Exponents And Powers - Question 20


Hence answer is 72

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