# Tag Archives: power

## Second Number Larger Than The First

Suppose a six-sided die has sides numbered through . If a person throws the die two times, what is the probability that the second number will be larger than the first? Source: NCTM Mathematics Teacher, September 2006 Solution The desirable … Continue reading

## Value of Sum

What is the value of the following sum? Source: NCTM Mathematics Teacher, September 2006 Solution The square bracket in the sum expression contains 1003 pairs of consecutive powers which pairwise sum to zero Answer:

## 2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

## Thirteen Power of (1+i)

If represents the imaginary unit, find real values for and such that . Source: NCTM Mathematics Teacher, October 2006 Solution Answer: Alternative solution Write the complex number in polar form Applying De Moivre’s theorem

## Exponent Value

What is the integer for which ? Source: NCTM Mathematics Teacher, October 2006 Solution Answer:

## Volumes of Two Cubes

The combined volumes of two cubes with integer side lengths are numerically equal to the combined lengths of their edges. What are the dimensions of the cubes? Source: NCTM Mathematics Teacher, January 2006 Solution Suppose is the side length of … Continue reading

## Perfect Squares and Perfect Cubes

List all integers less than that are both perfect squares and perfect cubes. Source: NCTM Mathematics Teacher, January 2006 Solution is a perfect square but not a perfect cube. On the other hand, is a perfect cube but not a … Continue reading

## Value of Exponent

What is the value of if ? Source: NCTM Mathematics Teacher, January 2006 SOLUTION Answer:

## Perfect Square

Find the smallest positive integer such that is a perfect square, is a perfect cube, and is a perfect fifth power. Source: NCTM Mathematics Teacher, December 2005 SOLUTION If is a perfect square, must have as a prime factor such … Continue reading

## Perfect Square

What is the smallest positive integer such that is a perfect square? Source: NCTM Mathematics Teacher, December 2005 SOLUTION will be smallest when we make the numerator as large a perfect square as it can be. Answer: