Test: Laws of Exponents - Class 9 MCQ

(64)^-3/2 = ( 8 )^{2 x - 3/2} =  (8)^-3  

= 1 / (8)³ = 1/ 512 

So option B is correct answer . 

Given,
first factorise 45 = 3² x 5¹
[3^(x-3)] 5^(x-4) = 45 = 3² (5¹)
On comparing both sides we get,
x-3 = 2 and x-4 = 1
By solving we get
=> x = 5
Hence, option A is the correct answer.

To solve this problem, we need to evaluate the expression (100 - 99⁰) x 100. Let's break it down step by step:
Step 1: Evaluate 99⁰: Any number raised to the power of 0 is equal to 1. So, 99⁰ = 1.
Step 2: Substitute the value of 99⁰ into the expression: (100 - 1) x 100 = 99 x 100.
Step 3: Multiply 99 and 100: 99 x 100 = 9900.
Therefore, the value of the expression (100 - 99⁰) x 100 is 9900.
Hence, the correct answer is C: 9900.

(25)^1/3=(5²)^1/3=(5)^2/3
5^2/3x5^1/3=5^3/3  = 5^2/3+1/3   = 5¹   [a^m x a ⁿ = a^(m+n)  ]
so answer is 5

(4²)^3/2 = (4)^{3/2 ×2} = (4)³ = 64

Using the quotient rule for exponents, (a^m / aⁿ) = a^{(m - n)}:

13^1/5 / 13^1/3 = 13^{(1/5 - 1/3)}
= 13^{1/5 - 1/3}
= 13 ^{3 - 5 / 15}
= 13^-2/15

Correct answer is D. 16.
= 

= (16)^{3/2  -  1/2}

= (16)¹

= 16.

Recognize that 8 can be expressed as 2³, as 2 x 2 x 2 = 8.
Rewrite 8^-5/3 as (2³)^-5/3
Apply the power of a power rule, which states that (a^m)ⁿ = a^mn. In this case,
multiply the exponents: 3 x -5/3
Simplify the expression.
Let's go through the steps:

(2³)^-5/3

(2)^-5

Now, 2^-5 means taking the reciprocal of 2⁵ (since a negative exponent indicates
reciprocal), so: 

2^-5 = 1/  2⁵

= 1/32  [ 2⁵ = 2x2x2x2x2 = 32 ]

Anything to the power 0 is always 1. 

The answer is 1 because of a⁰= 1.
So 1×1/1 = 1

(-1)^-1 =  - 1 / 1 = -1

81^1/2  can be written as (9) ^2x1/2 =  9 

49^1/2 can be written as  (7)^2x1/2 = 7

 ( 5 ) ^{3 x -1/3}   x  ( 5 ) ^{2  x -1/2} 

  ( 5 ) ^-1  x   ( 5 )  ^-1

   1 / 25 

- The expression  (a^m)ⁿ involves exponentiation rules.
- The rule for powers of a power is (a^m)ⁿ = a^mn
- This means you multiply the exponents when raising a power to another power.
-

- Very small numbers in standard form are expressed using negative exponents.
- Standard form is a way of writing numbers as a product of a number between 1 and 10, and a power of 10.
- For small numbers, the power of 10 is negative, indicating division by a power of 10.
- Example: 0.001 is written as 10^-3
- Negative exponents simplify representing very small values efficiently.