Q1. The answer is D. x4
Let's first rewrite the expression:
x⁵y²/xy² = x⁵/x * y²/y²
Using the rule xᵃ/xᵇ = x(ᵃ⁻ᵇ), we can write the expression as following:
x⁵y²/xy² = x⁵/x * y²/y² = x⁵⁻¹ * y²⁻² = x⁴ * y⁰ = x⁴ * 1 = x⁴
Thus, the correct answer is D.
Q2. The answer is A. 5(5^3/2/5)^2
125 in the form of exponent is 5³.
125 = 5³
Now, let's calculate all choices.
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ
A. 5(5³/2/5)² = 5 * (5³ * 5/2)²
= 5 * (5³⁺¹/2)²
= 5 * (5⁴/2)²
= 5 * (5⁴)²/(2)²
= 5 * 5⁴*²/4
= 5 * 5⁸ / 4
= 5¹⁺⁸ / 4
= 5⁹/4
≠ 5³ ≠ 125
B. (5³/5⁴)⁻³ = (5³⁻⁴)⁻³
= (5⁻¹)⁻³
= 5⁽⁻¹⁾*⁽⁻³⁾
= 5³
= 125
C. 5⁻²/5⁻⁵ = 5⁽⁻²⁾⁻⁽⁻⁵)
= 5⁽⁻²⁾⁺⁵
= 5³
= 125
D. 5(5⁵/5³) = 5 * 5⁵⁻³
= 5 * 5²
= 5¹⁺²
= 5³
= 125
Therefore, the only expression that is not equal to 125 is A.
Q3. The answer is 63x5
Let's check all choices
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ
A. 6³x
6³x/6x⁵ = 6³/6 * x/x⁵
= 6³⁻¹ * x¹⁻⁵
= 6²x⁻⁴
= 36x⁻⁴
≠ 36
B. 6³x⁵
6³x⁵/6x⁵ = 6³/6 * x⁵/x⁵
= 6³⁻¹ * x⁵⁻⁵
= 6² * x⁰
= 36 * 1
= 36
C. 6x⁵
6x⁵/6x⁵ = 1
≠ 36
D. 6⁷x⁵
6⁷x⁵/6x⁵ = 6⁷/6 * x⁵/x⁵
= 6⁷⁻¹ * x⁵⁻⁵
= 6⁶ * x⁰
= 46656 * 1
≠ 36
Therefore, the correct choice is B.
Q4. The answer is
We will use the rule: xᵃ/xᵇ = x(ᵃ⁻ᵇ)
5.4 x 10¹²/1.2 x 10³ = 5.4 / 1.2 x 10¹²/10³
= 4.5 x 10¹²⁻³
= 4.5 x 10⁹
Q5. The answer is B. To subtract powers with the same base, divide the exponents
Some of the rules regarding operations with exponents are:
xᵃ/xᵇ = x(ᵃ⁻ᵇ) - choice A
xᵃ * xᵇ = x(ᵃ⁺ᵇ) - choice C
(xᵃ)ᵇ = xᵃ*ᵇ - choice D
Through the process of elimination, choice B is not true.
