Question 1
Given [tex] \frac{x^5y^2}{xy^2} [/tex]
Substituting x = 0 and y = 0 gives [tex] \frac{(0)^5(0)^2}{(0)(0)^2}= \frac{0^7}{0^3}=0^{7-3}=0^4 [/tex]
Let's check option A
We have [tex]x^6y^5 = (0)^6(0)^5 = 0^{11}[/tex]
Let's check option B
We have [tex]x^5y=(0)^5(0)=0^6[/tex]
Let's check option C
We have [tex]x^4y = (0)^4(0) = (0)^{4+1} = 0^5[/tex]
Let's check option D
We have [tex]x^4 = (0)^4 = 0^4[/tex]
The expression that gives the same power with [tex] \frac{x^5y^2}{xy^2} [/tex] is the option D
Answer: Option D
------------------------------------------------------------------------------------------------------------
Question 2
We will check each option to see which one doesn't give the final value 125
Option A
[tex]5( \frac{5^ \frac{3}{2} }{5})^2 [/tex]
[tex]5( \frac{5^ \frac{3}{2} }{5})( \frac{5 \frac{3}{2} }{5}) [/tex]
[tex]5( \frac{5^{ \frac{3}{2}+ \frac{3}{2} }}{5^{1+1}}) [/tex]
[tex]5( \frac{5^ \frac{6}{2} }{5^2} )[/tex]
[tex]5( \frac{5^3}{5^2}) [/tex]
[tex]5(5^{3-2})[/tex]
[tex]5(5) = 25[/tex]
Option B
[tex]( \frac{5^3}{5^4})^{-3} [/tex]
[tex]( \frac{5^4}{5^3})^3 [/tex]
[tex](5^{4-3})^3[/tex]
[tex](5)^3 = 125[/tex]
Option C
[tex] \frac{5^{-2}}{5^{-5}} [/tex]
[tex] \frac{5^5}{5^2} [/tex]
[tex]5^{5-2} = 5^3 = 125[/tex]
Option D
[tex]5( \frac{5^5}{5^3}) [/tex]
[tex]5(5^{5-3}) = 5(5^2) = 5(25) = 125[/tex]
Answer: Option A
---------------------------------------------------------------------------------------------------------------
Question 3
Setting out the sum we have [tex] \frac{y}{6x^5} =36[/tex]
[tex]y = (36)(6x^5)[/tex]
[tex]y = (6^2)(6)(x^5)[/tex]
[tex]y = 6^3x^5[/tex]
Answer: Option B
------------------------------------------------------------------------------------------------------------
Question 4
Given [tex] \frac{5.4*10^{12}}{1.2^10^3} [/tex]
[tex] \frac{5.4}{1.2} * \frac{10^{12}}{10^3} [/tex]
[tex]4.5 * (10^{12-3})[/tex]
[tex]4.5 * 10^9[/tex]
Answer: Option B
-------------------------------------------------------------------------------------------------------------
Question 5
Option A is CORRECT - when you divide two powers with the same base, you'd subtract the power ⇒ 5³ ÷ 5² = 5³⁻² = 5¹
Option B is INCORRECT - When two powers with the same base are subtracted from each other, we'd have to work out the value of each base first before subtracting, i.e. 6³ - 6² = 216 - 36 = 180 ⇒ This isn't the same by doing [tex]6^{3/2}[/tex] which would give an answer of 14.7
Option C is CORRECT - Multiplying two powers with the same base is by adding the power, i.e. 4³ × 4² = 4³⁺² = 4⁵
Option D is CORRECT - Raising a power by a power is the same as multiplying the two powers, i.e. (12²)³ = 12⁽²⁾⁽³⁾ = 12⁶
ANSWER: Option B
