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Surds and Indices MCQs

Surds and Indices MCQs test the laws of exponents and roots, such as multiplying powers with the same base and simplifying negative or fractional powers. They appear in NTS, ECAT, SSC and bank aptitude papers. Each question has an instant answer, so you can check your simplification and learn the rules by heart.

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About Surds and Indices MCQs

This Aptitude topic is built on a few laws of indices. When powers with the same base are multiplied, the exponents are added; when divided, they are subtracted; a power raised to another power has its exponents multiplied; and a negative exponent means the reciprocal. Questions ask you to simplify expressions such as 256 to the power 0.16 times 256 to the power 0.09, find unknown exponents in equations like 5 to the power a equals 3125, and evaluate decimals raised to negative fractional powers. Writing every number as a power of a small base is the fastest approach.

Exams that include Surds and Indices MCQs

Pakistan

  • NTS
  • GAT
  • ISSB
  • Army/Navy/PAF initial tests
  • FPSC
  • PPSC
  • Banking job tests

India

  • SSC CGL
  • SSC CHSL
  • IBPS PO
  • SBI PO
  • RRB NTPC
  • Campus placements

Bangladesh

  • BCS
  • Bank job exams
  • Government job tests

Frequently asked questions

What are the basic laws of indices?

The main laws are: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m minus n), (a^m)^n = a^(mn), a^0 = 1 for non-zero a, and a^(minus n) = 1 ÷ a^n. A fractional power such as a^(1/2) means the square root of a.

How do you simplify (256)^0.16 × (256)^0.09?

Because the bases are the same, add the exponents: 0.16 + 0.09 = 0.25. So the expression equals 256 to the power one quarter, which is the fourth root of 256. Since 4 to the power 4 is 256, the answer is 4.

Last reviewed October 2026