Olympiad Test: Exponents And Powers - CAT MCQ

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

⇒ (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) 

 3^3x−5 = 3−2x ⇒ 3x−5 =−2x

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

⇒ 5x = 5

⇒ x = 1

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

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.

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.

2³ = 2x2x2 = 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).

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.

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.

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

(-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

Side of the square is 7 inches
So area of one square is  7² = 49
Total area of 5 such squares is
49×549×5 = 245 in²

2⁵/2^-6 = 2^5-(-6) = 2¹¹

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

= [(-2/3 )^-2 ]¹

= (-2/3)^-2
= [1 /  (-2/3)]²

= 9/4

a = 10, a² = 10²
10x10 =100

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.

Hence answer is 7²