Quantitative Aptitude
SURDS AND INDICES MCQs
Surds & Indices, Indices And Surds, Power
• In the given question, the expression (1000)^7 ÷ (10)^18 is to be evaluated.
• To solve this expression, the first step is to understand the meaning of the exponential terms used.
• Exponential terms are used to represent repeated multiplication of a number by itself.
• For example, (1000)^7 is the same as 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000.
• Similarly, (10)^18 is the same as 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
• To solve the given expression, the first step is to divide (1000)^7 by (10)^18.
• This can be done by using the property of exponents which states that if two exponential terms with the same base are divided, the exponents can be subtracted.
• Thus, (1000)^7 ÷ (10)^18 can be written as (1000)^7 ÷ (10)^18 = (1000)^7–18.
• Since 1000 is raised to the power 7–18, it is equal to 1000 raised to the power -11.
• This can be written as 1000–11 = 1000–11 = 1/1000–11.
• Thus, the answer to (1000)^7 ÷ (10)^18 is 1000–11 = 1/1000–11 = 1000.
• Therefore, option C. 1000 is the correct answer.
If you think the solution is wrong then please provide your own solution below in the comments section .
In order to determine whether 34n – 43n is divisible by 17 or not, we have to first understand the concept of divisibility. Divisibility is a concept of arithmetic in which a number can be divided by another number without leaving a remainder.
To determine whether 34n – 43n is divisible by 17 or not, we have to look at the expression 34n – 43n.
34n – 43n = -9n
Since -9n is a multiple of 9, it can be further simplified as:
-9n = -17 x (n/2)
Thus, -9n is divisible by 17. Therefore, 34n – 43n is also divisible by 17.
To summarize, the expression 34n – 43n is divisible by 17.
Explanation with relevant definitions and formulas:
Divisibility: Divisibility is a concept of arithmetic in which a number can be divided by another number without leaving a remainder.
Formula:
34n – 43n = -9n
-9n = -17 x (n/2)
Therefore, 34n – 43n is divisible by 17.
If you think the solution is wrong then please provide your own solution below in the comments section .
When a number is raised to a power, it is multiplied by itself a certain number of times. For example, 5 raised to the power of 3 (written as 5^3) means 5 multiplied by itself three times: 5 x 5 x 5 = 125.
To calculate (16)^1.75, we can use the following formula:
a^b = c
where a is the base number, b is the exponent, and c is the result.
Using this formula, we can write:
16^1.75 = c
We can also write 1.75 as a fraction: 7/4. This gives us:
16^(7/4) = c
To evaluate this expression, we can take the fourth root of 16 (which is 2) and raise it to the power of 7:
16^(1/4) = 2
2^7 = 128
Therefore, (16)^1.75 = 128, which corresponds to option C.
In summary, we used the formula a^b = c to calculate the value of (16)^1.75. We converted 1.75 to a fraction and used the properties of exponents to simplify the expression. Finally, we evaluated the expression to get the result of 128.