High School

IV. Laws of Exponent

31. What is the value of $3x^4 + 3x^4$?
A. 0
B. $3x^8$
C. $6x^4$
D. $6x^8$

32. What is the simplified form of $x^0$?
A. 0
B. 1
C. x
D. $x^1$

33. What is the simplified form of $5^4 * 5^2$?
A. 0
B. $5^2$
C. $5^6$
D. $5^8$

34. What is the result when $4^0$ is added to 2?
A. 2
B. 3
C. 4
D. 5

35. What is the result of $4x^2 - 3x^2$?
A. $x^2$
B. $7x^2$
C. $7x^4$
D. x

36. What is the value of $(2^3)^2$?
A. 8
B. 16
C. 24
D. 64

37. What is the simplified form of $(ab^2)^3$?
A. $a^3$
B. $ab^5$
C. $a^3b^6$
D. $a^4b^5$

38. What is the value of $ rac{4^5}{4^3}$?
A. 8
B. 12
C. 16
D. 20

39. What is the simplified form of $ rac{x^7}{x^5}$?
A. $x^2$
B. $x^5$
C. $x^7$
D. $x^{12}$

40. Which of the following represents $(3x^2)^3$?
A. $27x^6$
B. $9x^6$
C. $6x^6$
D. $3x^6$

Answer :

Let's address each of the questions one by one.


  1. What is the value of [tex]3x^4 + 3x^4[/tex]?



  • When you add like terms, you combine the coefficients. Here, [tex]3x^4 + 3x^4 = 6x^4[/tex]. The correct answer is C. [tex]6x^4[/tex].



  1. What is the simplified form of [tex]x^0[/tex]?



  • According to the laws of exponents, any non-zero number raised to the power of 0 is 1. Therefore, [tex]x^0 = 1[/tex]. The correct answer is B. 1.



  1. What is the simplified form of [tex]5^4 \times 5^2[/tex]?



  • When multiplying like bases, you add the exponents: [tex]5^{4+2} = 5^6[/tex]. The correct answer is C. [tex]5^6[/tex].



  1. What is the result when [tex]4^0[/tex] is added to 2?



  • [tex]4^0[/tex] equals 1 since any number raised to the power of 0 is 1. Therefore, [tex]1 + 2 = 3[/tex]. The correct answer is B. 3.



  1. What is the result of [tex]4x^2 - 3x^2[/tex]?



  • When you subtract like terms, subtract the coefficients: [tex]4x^2 - 3x^2 = 1x^2 = x^2[/tex]. The correct answer is A. [tex]x^2[/tex].



  1. What is the value of [tex](2^3)^2[/tex]?



  • When raising a power to another power, you multiply the exponents: [tex](2^3)^2 = 2^{3 \times 2} = 2^6 = 64[/tex]. The correct answer is D. 64.



  1. What is the simplified form of [tex](ab^2)^3[/tex]?



  • Distribute the exponent to both [tex]a[/tex] and [tex]b^2[/tex]: [tex]a^3b^{2 \times 3} = a^3b^6[/tex]. The correct answer is C. [tex]a^3b^6[/tex].



  1. What is the value of [tex]\frac{4^5}{4^3}[/tex]?



  • When dividing like bases, subtract the exponents: [tex]4^{5-3} = 4^2 = 16[/tex]. The correct answer is C. 16.



  1. What is the simplified form of [tex]\frac{x^7}{x^5}[/tex]?



  • When dividing like bases, subtract the exponents: [tex]x^{7-5} = x^2[/tex]. The correct answer is A. [tex]x^2[/tex].



  1. Which of the following represents [tex](3x^2)^3[/tex]?



  • Distribute the exponent to both 3 and [tex]x^2[/tex]: [tex]3^3x^{2 \times 3} = 27x^6[/tex]. The correct answer is A. [tex]27x^6[/tex].


These solutions apply laws of exponents which are fundamental in simplifying and solving expressions.

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