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• 1998 AJHSME Problems/Problem 16
  The power of <math>3</math> that <math>30</math> is closest to is <math>27=3^3</math>
  1 KB (206 words) - 17:52, 17 April 2021
• Trigonometric Equations
  To get rid of the fraction, both sides of the equation can be taken to the power of <math>-1</math>: Now take the <math>-1</math>th power of each side of the equation:
  8 KB (1,351 words) - 20:30, 10 July 2016
• 1984 AHSME Problems/Problem 11
  ...of a number is equivalent to raising the number to the <math> -1st </math> power. Therefore, taking the reciprocal of a number <math> x </math> and then squ
  1 KB (199 words) - 10:55, 21 July 2015
• 2003 AMC 12A Problems/Problem 20
  Note that answer choices B and E have a power of 3 in them, which is impossible since every letter only has 2 options due
  3 KB (434 words) - 01:12, 12 April 2023
• 1996 AJHSME Problems/Problem 7
  ...ish by two powers of <math>2</math>, while increasing Gretel's fish by one power of <math>2</math>.
  2 KB (264 words) - 11:26, 27 June 2023
• 1997 AHSME Problems/Problem 26
  The product of two lengths with a common point brings to mind the [[Power of a Point Theorem]]. Finally, we apply the power of a point theorem to point <math>D</math>. This states that <math>AD \cdo
  3 KB (513 words) - 18:24, 6 November 2022
• 1994 AJHSME Problems/Problem 10
  ...math>36</math> to get <math>2^2*3^2</math>. Then add <math>1</math> to the power of both <math>2</math> and <math>3</math> to get <math>3</math>. Multiply <
  1 KB (195 words) - 08:42, 26 May 2021
• 2016 AMC 10A Problems/Problem 20
  ...r variables <math>a, b,c,</math> and <math>d</math>, each to some positive power. What is <math>N</math>? ...he number of terms that have all <math>a,b,c,d</math> raised to a positive power is <math>\binom{N-1}{3}+\binom{N-2}{3}+\cdots + \binom{4}{3}+\binom{3}{3}=\
  4 KB (630 words) - 15:13, 8 October 2023
• Decimal
  ...can be done because both the numerator and denominator is multiplied by a power of 10. Afterward, we can proceed like a decimal divided by an integer.
  5 KB (714 words) - 17:48, 12 June 2020
• 1985 AHSME Problems/Problem 27
  and as <math>3</math> is not a perfect power, we deduce that <math>x_n</math> is an integer if and only if the exponent,
  2 KB (316 words) - 02:06, 20 March 2024
• 2011 AMC 8 Problems/Problem 22
  7 to the power of 2 is 49. So, the tens digit is 4. 7 to the power of 3 is 343. So, the tens digit is 4.
  2 KB (324 words) - 21:54, 15 January 2024
• Mock Geometry AIME 2011 Problems/Problem 3
  ...math>, we have <math>BD \times BA=BP \times BQ=2 \times 4=8</math>. By the Power of a Point on <math>C</math>, we have <math>CE \times CA=CQ \times CP=5 \ti
  1 KB (231 words) - 22:05, 23 December 2022
• Mock Geometry AIME 2011 Problems/Problem 5
  Now, from Power of a Point on <math> D </math>, we have <math> BD^2\cdot DC^2=AD^2\cdot DE^ ...>BD=\frac{36*40}{36+44} = 18, CD = \frac{44*40}{36+44}=22.</math> Then, by power of a point on <math>D,</math> we have
  4 KB (665 words) - 03:40, 25 December 2022
• Mock Geometry AIME 2011 Problems/Problem 7
  ...herefore, <math>\cos{\angle E} = \frac{EB}{EA}=\frac{5}{13}</math>. By the Power of a Point of <math>E</math>, <math>EP^2=EB*EC=\frac{5}{4}*\frac{125}{4}</m
  2 KB (311 words) - 21:38, 3 January 2012
• 1950 AHSME Problems/Problem 37
  ...</math>. Rewriting: <math>a^y=x</math> such that <math>x<a</math>. Well, a power of <math>a</math> can be less than <math>a</math> only if <math>y<1</math>.
  2 KB (313 words) - 17:09, 15 March 2017
• 1950 AHSME Problems/Problem 42
  ...one <math>x</math> to the start and then taking that <math>x</math> to the power of <math>y</math> does not have an effect on the equation, since <math>y</m
  1 KB (234 words) - 01:21, 14 January 2023
• 2012 AMC 12A Problems/Problem 20
  ...lying them all together. Therefore, we pick a power of <math>x</math> or a power of <math>2</math> from each factor.
  2 KB (298 words) - 20:59, 5 February 2019
• 2012 AMC 12A Problems/Problem 16
  ...ath>. We now have <math>AZ=YZ=7</math> and <math>XA=6</math>. Consider the power of point <math>Z</math> with respect to Circle <math>O,</math> we have <mat
  9 KB (1,496 words) - 02:40, 2 October 2022
• 2012 AMC 12A Problems/Problem 18
  We can use POP(Power of a point) to solve this problem. First, notice that the area of <math>\tr
  4 KB (717 words) - 19:07, 28 July 2021
• 2012 AMC 12A Problems/Problem 24
  ...l function), and <math>g(x) = x^k</math> for <math>k > 0</math>(increasing power function for positive <math>x</math>). <math>f(x)</math> is used to establi
  5 KB (870 words) - 11:38, 31 March 2024

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