Exponents
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40 free Exponents trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Exponents are shorthand for repeated multiplication, and they are how mathematics copes with the very large and the very small. A few small raised numbers can describe a grain count that outgrows a kingdom, the memory inside a computer, or the distance light travels in a year. This quiz mixes practice with trivia. Expect the exponent rules for multiplying, dividing and raising powers, what a zero or negative exponent means, how a negative base behaves, expressions to simplify, the shorthand scientists use for huge and tiny numbers, and a set of word problems about doubling, decay and scale. Alongside them are the stories: who invented the notation, where the vocabulary comes from, and the legends and records that show how quickly powers grow. It suits students revising for a test, teachers who want a ready-made class quiz, and adults curious about how much school math has stuck. Every question comes with its answer and a short explanation.
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Q 01Which name did a nine-year-old boy coin for the number 10¹⁰⁰?
Googol
Googol was the invention of Milton Sirotta, nephew of mathematician Edward Kasner, and the search engine Google later took its name from a respelling of it.
Q 02In a famous legend about doubling, grains of wheat are laid one, two, four and so on across the squares of what?
A chessboard
A chessboard filled this way would hold 2⁶⁴ − 1 grains, more than 18 quintillion, and in some tellings the ruler has the inventor who asked for them executed.
Q 03Which French philosopher, namesake of Cartesian coordinates, introduced today's raised-number notation for powers?
René Descartes
René Descartes set out the notation in La Géométrie in 1637, yet he kept writing squares the long way, as a letter repeated twice.
Q 04Any nonzero number raised to the power of zero, whether 9⁰ or 25⁰, always equals which value?
1
1 is the result because dividing a power by itself, such as 9² ÷ 9², subtracts the exponents to leave 9⁰, and any number divided by itself is 1.
Q 05Which rule of thumb, named after an Intel co-founder, says transistor counts on a chip double about every two years?
Moore's law
Moore's law began as a 1965 magazine forecast of doubling every year, an exponential pace that Gordon Moore himself slowed to every two years in 1975.
Q 06In Einstein's famous equation E = mc², the exponent 2 tells you to square which physical quantity?
Speed of light
Speed of light squared is so enormous that a single kilogram of mass corresponds to roughly 10¹⁷ joules of energy.
Q 07Which scale, introduced in 1935, rises by one whole number for every tenfold jump in recorded wave amplitude?
Richter
Richter magnitudes hide even bigger leaps in energy, since each whole-number step means about 31.6 times more energy released.
Q 08Which household product did Britney Gallivan fold in half twelve times in 2002, beating a supposed limit of eight?
Toilet paper
Toilet paper did the job, a single strip 4,000 feet long, because every fold doubles the layers and twelve folds stack 4,096 of them.
Q 09Which French lawyer wrote in a book margin that aⁿ + bⁿ = cⁿ has no whole-number solutions for exponents above 2?
Pierre de Fermat
Pierre de Fermat left no proof behind, and the claim resisted every mathematician for 358 years until Andrew Wiles settled it in 1994.
Q 10Which puzzle of discs stacked on three pegs takes at least 2ⁿ − 1 moves to solve when it has n discs?
Tower of Hanoi
Tower of Hanoi went on sale in 1883 with a legend of temple priests shifting 64 golden discs, a task whose completion would end the world.
Q 11Multiplying powers of one base, three a's then four more, a³ × a⁴ simplifies to which power?
a⁷
a⁷ is right because the bases match, so the exponents add: three factors of a and four more make seven in all. Multiplying 3 by 4 to get a¹² is the classic slip.
Q 12Raising a power to another power, as in (y²)⁵, five groups of two y's, gives which simplified expression?
y¹⁰
y¹⁰ follows because raising a power to a power multiplies the exponents, 2 × 5. Adding them to get 7 confuses this with the rule for multiplying like bases.
Q 13Dividing powers of one base, m⁸ ÷ m² cancels two m's from the top and leaves which power?
m⁶
m⁶ is what remains, since dividing like bases subtracts the exponents, 8 − 2. Dividing the exponents instead gives the tempting wrong answer m⁴.
Q 21A byte holds eight bits, each a 0 or a 1, so 2⁸ gives how many different values it can store?
256
256 values run from 0 to 255, and the eight-bit byte became the standard partly because eight is itself a convenient power of two.
Q 22IPv4 internet addresses are 32 bits long, so 2³² allows roughly how many unique addresses?
4.3 billion
4.3 billion is fewer than one address for every person on Earth, which is why the pool ran dry and a successor with 128-bit addresses, IPv6, was drawn up in the 1990s.
Q 23One bacterium splits in two every 20 minutes; after three hours of such doubling, how many bacteria are there?
512
512 bacteria is 2⁹, one doubling for each of the nine 20-minute periods in three hours. Three more hours at that pace would take the count past a quarter of a million.
Q 14In the power 5⁻², which equals 1/25, the negative exponent tells you to take which of these?
The reciprocal
The reciprocal is what a negative exponent calls for, so 5⁻² flips to 1 over 5². The result here is a small positive fraction, not a number below zero.
Q 15Written as a decimal, 10⁻³ equals which number, the same size as the metric prefix milli?
0.001
0.001 is one thousandth, because 10⁻³ means 1 divided by 10³, which is why a millimetre is a thousandth of a metre.
Q 16A negative base raised to an even exponent, such as (−2)⁴, always gives which kind of result?
Positive
Positive is guaranteed, because the minus signs cancel in pairs: (−2)⁴ is 16. That is also why no real number squared can come out below zero.
Q 17In written mathematics, −3² with no brackets is read as which value, since the exponent acts before the minus sign?
−9
−9 is the standard reading, yet type −3^2 into Microsoft Excel and the spreadsheet squares the negative number first and returns 9.
Q 18The exponent in (3x)² applies to every factor inside the brackets, so the expression expands to which of these?
9x²
9x² is the expansion, since both the 3 and the x are squared. Squaring only the x gives 3x², the slip the brackets are there to prevent.
Q 19The mnemonic PEMDAS, whose E stands for exponents, helps students remember which set of rules?
Order of operations
Order of operations puts exponents second, straight after parentheses, and British schools teach the same sequence as BIDMAS, with I for indices.
Q 20Which way of writing numbers turns 300,000,000 into 3 × 10⁸, using a power of 10 to keep huge values short?
Scientific notation
Scientific notation goes by the name standard form in Britain, and calculators shorten it with the letter E, so 3 × 10⁸ can show as 3E8.
Q 24After three half-lives, a radioactive sample has halved three times over; which fraction of the original is left?
One eighth
One eighth is left, because each half-life multiplies what remains by ½ and (½)³ is 1/8. Wait ten half-lives and less than a thousandth survives.
Q 25Dating ancient bones and wood relies on the exponential decay of which isotope, which halves about every 5,730 years?
Carbon-14
Carbon-14 dating won Willard Libby the 1960 Nobel Prize in Chemistry, and it stops working at about 50,000 years, when too little of the isotope is left to measure.
Q 26Under the inverse-square law, moving three times farther from a lamp cuts its brightness to which fraction?
One ninth
One ninth is all that arrives, because the same light spreads over a sphere whose area grows with the square of the distance, and 3² is 9.
Q 27Which finance shortcut divides a number by the interest rate to estimate the years money needs to double?
Rule of 72
Rule of 72 works because compound interest is exponential growth: at 6 percent a year, savings double in about 12 years.
Q 28Doubling every edge of a cube multiplies its volume by how much, because 2 is raised to the third power?
8 times
8 times the volume comes with only 4 times the surface area, a mismatch that Galileo first described in 1638 and that still limits how far aircraft can be scaled up.
Q 29Which design couple, makers of a famous lounge chair, directed the 1977 film Powers of Ten about cosmic scale?
Charles and Ray Eames
Charles and Ray Eames pull the camera back ten times farther every ten seconds from a Chicago picnic, then dive inward to the quarks inside a single proton.
Q 30The number 6.022 × 10²³, the count of particles in one mole of a substance, honours which Italian scientist?
Amedeo Avogadro
Amedeo Avogadro never saw the number that carries his name: he died in 1856, nine years before anyone first estimated it.