Which of the following is equivalent to x^5y^2/xy^2 when x=0 and y = 0?A. X^6y^5B.x^5yC.x^4yD.x^4Which expression is NOT equal to 125A.5(5^3/2/5)^2B.(5^3/5^4)^-3C. 5^-2/5^-5D. 5(5^5/5^3)A fraction reduces to 36. If it’s denominator is 6x^5. What is it’s numerator?A.6^3xB. 6^3x^5C.6x^5D.6^7x^5Which is the correct simplification of 5.4x10^12/1.2x10^3 written in scientific notation A. 4.5x10^7B.4.5x10^9C. 45x10^6D. 6.48x10^7Which of the following statements is NOT true regarding operations with exponents? A. To divide powers with the same base, subtract the exponents B. To subtract powers with the same base, divide the exponents C. To multiply powers with the same base , add the exponents D. To raise a power to a power, multiply the exponents

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
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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
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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
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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
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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