A reliable method
Rewrite powers with a common base where possible. For repeated doubling, count completed intervals. Separate a principal root from the solutions of a squared equation.
The common trap
Adding exponents applies to multiplication of like bases, not addition of powers. A negative sign outside a square is different from a negative base inside it.
Check the conclusion
Check a short sequence of powers to establish the cycle and use the exponent remainder to select the position. Estimate magnitude before choosing an exact result.
Contrast the cases
A quantity beginning at three and doubling four times follows 3,6,12,24,48. The initial observation is not itself a doubling. Likewise 2⁷/4 is 2⁵=32, because 4 is 2²; subtracting four from the exponent applies the wrong transformation. Powers of seven have units digits 7,9,3,1, so an exponent with remainder two modulo four selects 9.
Transfer and explain
Transfer: find the last digit of 7⁸ and calculate a quantity starting at five after three doublings. The results are 1 and 40. Explain why the first question depends only on a cycle while the second retains the starting amount.
What is the value of 2^7 divided by 4?
- Write 4 as 2².
- When dividing powers with the same nonzero base, subtract exponents.
- The result is 2^5 = 32.
Compare the other answer choices
Subtracts the denominator itself from the exponent.
Omits the division.
Adds exponents instead of subtracting.
Divides the exponent instead of the exponential value.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GMAT exam contentSiyavula Grade 10 mathematics foundation reference