Multiplication and Division of Powers, Free Math Test

Question 1 (1 point)

Simplify: [tex](3^2)^4(a^2)^3[/tex]

[tex]3^8a^6[/tex]

[tex]3^6a^8[/tex]

[tex]3^6a^6[/tex]

[tex]3^8a^8[/tex]

Question 2 (1 point)

Which of the following expressions is equal to [tex]x^{12}[/tex]?

[tex]x^3x^4[/tex]

[tex](x^3)^4[/tex]

[tex]x^6+x^6[/tex]

[tex]\dfrac{x^{24}}{x^2}[/tex]

Question 3 (1 point)

Simplify: [tex](x^2)^3(x^4)^5x[/tex]

[tex]x^{26}[/tex]

[tex]x^{120}[/tex]

[tex]x^{27}[/tex]

[tex]x^{15}[/tex]

Question 4 (1 point)

Simplify: [tex](2x^3)^4[/tex]

[tex]2x^{12}[/tex]

[tex]8x^{12}[/tex]

[tex]16x^7[/tex]

[tex]16x^{12}[/tex]

Question 5 (2 points)

Find [tex]n[/tex] if [tex]x^5x^n = x^{12}[/tex].
[tex]n =[/tex]

Question 6 (1 point)

Simplify: [tex](2^3)^2(4^3)(a^4)^5[/tex]

[tex]2^9a^{20}[/tex]

[tex]2^{12}a^{20}[/tex]

[tex]2^{12}a^9[/tex]

[tex]8^9a^{20}[/tex]

Question 7 (1 point)

Which of the following equalities is false?

[tex](2^3)^4=2^{12}[/tex]

[tex](2^5)^2=4^5[/tex]

[tex](3^2)^4(3^2)^7=3^{24}[/tex]

[tex]\dfrac{(3^4)^2}{3^2}=3^6[/tex]

Question 8 (1 point)

Simplify: [tex]\dfrac{2^3x^4}{2^4x^3}[/tex]

[tex]\dfrac{x}{2}[/tex]

[tex]\dfrac{2}{x}[/tex]

[tex]\dfrac{1}{2x}[/tex]

[tex]2x[/tex]

Question 9 (2 points)

Find [tex]n[/tex] if [tex](a^3)^n = a^{15}[/tex].
[tex]n =[/tex]

Question 10 (1 point)

Simplify: [tex]\dfrac{-2x^3y}{2^5x}[/tex]

[tex]-\dfrac{x^2}{2^4}[/tex]

[tex]-\dfrac{x^2y}{2^3}[/tex]

[tex]\dfrac{x^2y}{2^4}[/tex]

[tex]-\dfrac{x^2y}{2^4}[/tex]

Question 11 (1 point)

Simplify: [tex]\dfrac{6a^4b^2}{2a^4b}[/tex]

[tex]4b[/tex]

[tex]3ab[/tex]

[tex]3b[/tex]

[tex]3a^8b^3[/tex]

Question 12 (1 point)

Simplify: [tex]\left(\dfrac{x^2}{3}\right)^3[/tex]

[tex]\dfrac{x^6}{27}[/tex]

[tex]\dfrac{x^6}{3}[/tex]

[tex]\dfrac{x^5}{27}[/tex]

[tex]\dfrac{x^6}{9}[/tex]

Question 13 (2 points)

Evaluate: [tex]\dfrac{5^7 \times 5^3}{5^8} =[/tex]

Question 14 (1 point)

Which of the following equalities is false?

[tex]\dfrac{x^2}{x^4y^2}=\dfrac{1}{x^2y^2}[/tex]

[tex]\dfrac{x^6}{x^2y^2}=\dfrac{x^3}{y^2}[/tex]

[tex]\dfrac{3^3x^2}{x^4y^2}=\dfrac{3^3}{x^2y^2}[/tex]

[tex]\dfrac{3^3x^2}{3^2x^4y^2}=\dfrac{3}{x^2y^2}[/tex]

Question 15 (2 points)

The edge of a cube is [tex]2^3[/tex] inches long, and its volume is [tex]2^n[/tex] cubic inches. Find [tex]n[/tex].
[tex]n =[/tex]

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