Exponents and Radicals Quiz

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1. Simplify 3^x – 3^x-1 – 3^x-2

A. 3^x-2

B. 3^3x-3

C. 5 x 3^x-2

D. 13 x 3^x

2. Solve for x: [x – √(1-x)]^1/2 = 1 - √x.

A. -16/25 & 0

B. 25/16 & 0

C. -25/16 & 0

D. 16/25 & 0

3. Simplify:

[(x²y³z^-2)^-3 (x^-3yz³)^-1/2] ÷ (xyz^-3)^-5/2

A. 1/x²y⁷z³

B. 1/x²y⁷z⁵

C. 1/x²y⁵z³

D. 1/x⁵y⁷z³

4. Find x from the following equations:

27^x = 9^y

81^y3^-x = 243

A. 2.5

B. 2

C. 1

D. 1.5

5. (xy^-1 / x^-2y³)⁴ ÷ (x²y^-2 / x^-3y³)³

A. xy³

B. y/x³

C. x³y

D. 1/x³y

6. If 9^x = 5, what is the value of 3^4x?

A. 5

B. 15

C. 25

D. 35

7. Transform the fraction by rationalizing the denominator

4x / [x - (x² – 4)^1/2]

A. x[x + (x²-4)^1/2]

B. x(x²-4)^1/2

C. 4x - (x²-4)^1/2

D. x + (x²-4)^1/2

8. Rationalize the denominator and determine the transformed fraction a^1/2 ÷ (a^1/2 - a^1/2 b^1/2)

A. (1 + b^1/2) ÷ (1 – b)

B. (a + b^1/2) ÷ (1 – b)

C. (a + b) ÷ (a – b)

D. (√a + b) ÷ (√b + a)

9. Solve for x: 3^x5^x+1 = 6^x+2

A. 2.1455

B. 2.1445

C. 2.4154

D. 2.1544

10. Solve for a from the following equations:

(a^m)aⁿ) = 100000                a^mn = 100000     aⁿ/a^m = 10

A. 15.85

B. 10

C. 1

D. 12.56

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