Review of Integer Exponents and Square Roots
Read this topicExplanations 4
- Consider evaluating the exponent aba^bab as follows for a positive integer bbb: multiply the integer aaa by itself bbb times. For instance: 22=2×2=42^2 = 2 \times 2 = 422=2×2=4 …
By Joshua Siktar, Expii Team, Victor Wang, Jonathan Heller
- Exponentiation is used to express iterated multiplication, much like multiplication is used to express iterated addition. Exponentiation is most naturally understood with integr…
By Leland Reardon, Qinzhuo Zhang, Expii Team, Victor Wang, Jonathan Heller
- Basic Properties of Exponents When you have a number of the form aba^bab the bbb is the exponent and that means that aaa will be multiplied bbb times to evaluate aba^bab. Now th…
By Tarang Saluja
- What is an Exponent? An exponent is the power to which a value is to be raised. For example, in the term 232^323, 333 is considered the exponent that 222 is being raised to. Thi…
By Sarah Walker
Problems 22
- 8+25−36+12=?\sqrt{8} + 2\sqrt{5} - \sqrt{36} + \sqrt{12} = ?8+25−36+12=?
- Compute (26)⋅(24)(2 \sqrt 6) \cdot (\sqrt{24})(26)⋅(24).
- What is the product of 14\sqrt{14}14 and 2016\sqrt{2016}2016?
- Simplify the following expression: (1+5)23+32+42\frac{(1 + \sqrt{5})^2}{3 + \sqrt{\sqrt{3^2 + 4^2}}}3+32+42(1+5)2
- What is 75+147\sqrt{75} + \sqrt{147}75+147?
- What is 288−200\sqrt{288} - \sqrt{200}288−200?
- The expression 5!5!5!, or "555 factorial," is equal to 1⋅2⋅3⋅4⋅51 \cdot 2 \cdot 3 \cdot 4 \cdot 51⋅2⋅3⋅4⋅5. What is 1⋅2⋅3⋅4⋅5\sqrt{1} \cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{4…
- Simplify the following expression: ∏i=143i\sqrt{\prod_{i=1}^4 3^i}i=1∏43i (If you're not sure what that ∏\prod∏ symbol means, click here to learn more about it!)
- If xxx and yyy are positive numbers with x20=y4x^{20} = y^4x20=y4, then what is x35x^{35}x35 in terms of yyy?
- Let a,b,c∈Ra,b,c \in \mathbb{R}a,b,c∈R. Which of the following are true about exponentiation?
- There is only one pair of integers (a,b)(a,b)(a,b) such that a<ba < ba<b and ab=baa^b = b^aab=ba. What is this pair?
- What is the value of the following expression? 22222^{2^{2^2}}2222 (Hint: evaluate the exponents from the top down. This is equal to 2242^{2^4}224, not 4224^{2^2}422.)
- 34−43=3^4 - 4^3 =34−43=
- Define a sequence such that a1=1a_1 = 1a1=1 and for all n≥2n \ge 2n≥2, an=(an−1)na_n = (a_{n-1})^nan=(an−1)n. What is a274a_{274}a274?
- What is 45⋅2−84^5 \cdot 2^{-8}45⋅2−8?
- ∑i=14i(i−1)=\sum_{i=1}^4 i^{(i-1)} =i=1∑4i(i−1)=
- What is the smallest positive integer nnn such that n(n−1)−(n−1)n≠1n^{(n-1)} - (n-1)^n \not= 1n(n−1)−(n−1)n=1?
- If x=63x = 6^3x=63, what is 666^666 in terms of xxx?
- What is 174\sqrt{17}^4174?
- Simplify the following expression: 3×(25)23 \times (\sqrt{25})^23×(25)2
- A world-renowned author can write 565^656 words per day. If he needs to finish his book, which is 5105^{10}510 words, how many days does he need to work?
- What is the length of each wall, to the nearest whole foot? Does the non-profit pass inspection?