This GRE maths sample question is a Numeric Entry question in Number Properties. Concept tested: Rules of Exponents.

Question 10: If (3^{-22} + 3^{-19} + 3^{-17} + 3^{-16}) = k(3^{-24}), what is k?

From INR 2999

**Given**: (3^{-22} + 3^{-19} + 3^{-17} + 3^{-16}) = k(3^{-24})

Taking 3^{-22} common from both sides,

3^{-22}(1 + 3^{3} + 3^{5} + 3^{6}) = k(3^{-22}(3^{-2}))

**Divide both sides of the equation by 3 ^{-22}**

1 + 3

1 + 27 + 243 + 729 = k(3

1000 = k(3

**Multiply both sides of the equation by 3( ^{2})**

3

→ k = 9000.

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