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10 Must-Do Exponent Questions for GMAT DS: Mastering Quantitative Reasoning

Yasunari Kawabata

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Embark on a journey to conquer the intricacies of exponents in GMAT's Quantitative Reasoning section with our meticulously curated list of 10 must-do questions. These challenges will not only sharpen your problem-solving abilities but also propel you towards a stellar GMAT score. Dive into the realm of exponents and unlock the secrets of advanced mathematics.

Question 1: Exponents and Multiplication

Question 1: Exponents And Multiplication 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

10 Must Do Exponent Questions for GMAT DS (10 Must Do Questions)

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Solve for x: 2^x * 2⁵ = 2¹²

Solution: Combine the exponents when multiplying terms with the same base. 2^x * 2⁵ = 2^x+5 = 2¹². Therefore, x = 12 - 5 = 7.

Question 2: Exponents and Division

Question 2: Exponents And Division 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Simplify: (3⁴)² / 3⁶

Solution: Apply the exponent rule (a^b)^c = a^b*c. (3⁴)² = 3^4*2 = 3⁸. Divide by 3⁶ to get 3⁸ / 3⁶ = 3^8-6 = 3² = 9.

Question 3: Exponents and Powers of Powers

Question 3: Exponents And Powers Of Powers 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Evaluate: (2³)⁴

Solution: Multiply the exponents when raising a power to another power. (2³)⁴ = 2^3*4 = 2¹² = 4096.

Question 4: Exponents and Zero Exponents

Question 4: Exponents And Zero Exponents 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Solve for x: 5^x = 1

Solution: Any number raised to the power of 0 equals 1. Therefore, x = 0.

Question 5: Exponents and Negative Exponents

Question 5: Exponents And Negative Exponents 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Simplify: 2^-3

Solution: A negative exponent indicates the reciprocal of the base raised to the positive exponent. 2^-3 = 1/2³ = 1/8.

Question 6: Exponents and Scientific Notation

Question 6: Exponents And Scientific Notation 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Express 0.000005 in scientific notation.

Solution: Move the decimal point 6 places to the right and adjust the exponent accordingly. 0.000005 = 5 * 10^-6.

Question 7: Exponents in Real-World Applications

Question 7: Exponents In Real World Applications 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

A population of bacteria grows exponentially, doubling every hour. If there are initially 100 bacteria, how many bacteria will there be after 5 hours?

Solution: The growth pattern can be represented by the equation P = 100 * 2^h, where P is the population size and h is the number of hours. After 5 hours, P = 100 * 2⁵ = 3200 bacteria.

Question 8: Exponents and Inequalities

Question 8: Exponents And Inequalities 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Solve the inequality: 3^x < 27

Solution: Rewrite 27 as 3³ and compare the exponents. x < 3.

Question 9: Exponents and Logarithms

Question 9: Exponents And Logarithms 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Find the value of log₃ 81.

Solution: The logarithm is the exponent to which the base must be raised to get the given number. log₃ 81 = 4 because 3⁴ = 81.

Question 10: Exponents and Complex Numbers

Question 10: Exponents And Complex Numbers 10 Must Do Exponent Questions For GMAT DS (10 Must Do Questions)

Simplify: (√-1)⁶

Solution: (-1)⁶ = 1 and √-1 represents the imaginary unit i. Therefore, (√-1)⁶ = i⁶ = i⁴ * i² = 1 * (-1) = -1.

Mastering exponents is a cornerstone of success in GMAT's Quantitative Reasoning section. These 10 must-do questions provide a comprehensive foundation, equipping you with the knowledge and problem-solving skills to tackle even the most challenging exponent-related problems. Practice diligently, seek guidance from experts, and embrace the power of exponents to unlock your full potential on GMAT DS.