Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
6001	Rationalize the Denominator	fourth root of (5x)/x	$\sqrt[4]{\frac{5 x}{x}}$
6002	Simplify	(x^3+2x^2+1)(x^2+5)	$(x^{3} + 2 x^{2} + 1) (x^{2} + 5)$
6003	Write with Rational (Fractional) Exponents	fourth root of 2^-5	$\sqrt[4]{2^{- 5}}$
6004	Write in Standard Form	3x(x-7)(x-1)^2	$3 x (x - 7) {(x - 1)}^{2}$
6005	Simplify	(x^(1/3)*x^(5/6))/(x^(1/6))	$\frac{x^{\frac{1}{3}} \cdot x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$
6006	Solve for x	3/(x+3)-2/(x-1)=-1/(x^2+2x-3)	$\frac{3}{x + 3} - \frac{2}{x - 1} = - \frac{1}{x^{2} + 2 x - 3}$
6007	Find the Domain and Range	x=(y+1)^3-2	$x = {(y + 1)}^{3} - 2$
6008	Convert to Radical Form	33gh^(1/2)	$33 g h^{\frac{1}{2}}$
6009	Evaluate	(-3x*(x)^(1/2))/((1-3x^2)^(1/2))-((1-3x^2)^(1/2))/(2(x)^(1/2))	$\frac{- 3 x \cdot {(x)}^{\frac{1}{2}}}{{(1 - 3 x^{2})}^{\frac{1}{2}}} - \frac{{(1 - 3 x^{2})}^{\frac{1}{2}}}{2 {(x)}^{\frac{1}{2}}}$
6010	Solve the Inequality for y	2x-y>10	$2 x - y > 10$
6011	Simplify	square root of (x^5y^2)/(125xy)	$\sqrt{\frac{x^{5} y^{2}}{125 x y}}$
6012	Add	(5x^4-3x^2+4)+(6x^3-4x^2-7)	$(5 x^{4} - 3 x^{2} + 4) + (6 x^{3} - 4 x^{2} - 7)$
6013	Solve the System of Equations	3y+x^2-4x-17=0 3y-10x+38=0	$3 y + x^{2} - 4 x - 17 = 0$ $3 y - 10 x + 38 = 0$
6014	Find the Inverse	f(x)=1/2(3-3x)	$f (x) = \frac{1}{2} (3 - 3 x)$
6015	Simplify	-10i^30+8i^57+i^88+10i^34	$- 10 i^{30} + 8 i^{57} + i^{88} + 10 i^{34}$
6016	Simplify	(2- square root of 3)/(-2- square root of 5)	$\frac{2 - \sqrt{3}}{- 2 - \sqrt{5}}$
6017	Find the Degree, Leading Term, and Leading Coefficient	f(x)=-2x^4-3x^2+2x+7x^5	$f (x) = - 2 x^{4} - 3 x^{2} + 2 x + 7 x^{5}$
6018	Simplify	square root of cube root of 27	$\sqrt{\sqrt[3]{27}}$
6019	Write with Rational (Fractional) Exponents	( square root of x)^2	${(\sqrt{x})}^{2}$
6020	Simplify	(3^-4*3^-1)/3	$\frac{3^{- 4} \cdot 3^{- 1}}{3}$
6021	Solve for b	log base b of 2=1	$\log_{b} (2) = 1$
6022	Solve for g	(g+3)/(g-2)=56/21	$\frac{g + 3}{g - 2} = \frac{56}{21}$
6023	Simplify	- square root of (1-cos(7A))/2	$- \sqrt{\frac{1 - \cos (7 A)}{2}}$
6024	Find the Reference Angle	cos(pi/3)	$\cos (\frac{π}{3})$
6025	Evaluate the Limit	limit as x approaches infinity of (5+x-4x^2)/( square root of 1+x^2+2x^4)	$lim_{x \to \infty} \frac{5 + x - 4 x^{2}}{\sqrt{1 + x^{2} + 2 x^{4}}}$
6026	Simplify	(5a^2xy^3)(b^3y^4)^3	$(5 a^{2} x y^{3}) {(b^{3} y^{4})}^{3}$
6027	Evaluate	square root of x+10-9=-7	$\sqrt{x + 10} - 9 = - 7$
6028	Graph	f(x)=2* log base 1/4 of x	$f (x) = 2 \cdot \log_{\frac{1}{4}} (x)$
6029	Simplify	((5pr^-2)^-2)/((3p^-1r)^3)	$\frac{{(5 p r^{- 2})}^{- 2}}{{(3 p^{- 1} r)}^{3}}$
6030	Simplify	4/( square root of 5a)-2/( square root of 5a)-(7 square root of 5a)/(5a)	$\frac{4}{\sqrt{5 a}} - \frac{2}{\sqrt{5 a}} - \frac{7 \sqrt{5 a}}{5 a}$
6031	Verify the Identity	n root of a/b=(n root of a)/(n root of b)	$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
6032	Simplify	(12x^-5y^3)/(3^-2x^-2y^-4)	$\frac{12 x^{- 5} y^{3}}{3^{- 2} x^{- 2} y^{- 4}}$
6033	Solve for y	log base 1/6 of 1/1296=y	$\log_{\frac{1}{6}} (\frac{1}{1296}) = y$
6034	Determine if a Polynomial	-7x^5+8x-4x^3+2x^4	$- 7 x^{5} + 8 x - 4 x^{3} + 2 x^{4}$
6035	Solve for y	x=3 log of y^2	$x = 3 \log (y^{2})$
6036	Graph	f(x)=5* log of -x	$f (x) = 5 \cdot \log (- x)$
6037	Find Amplitude, Period, and Phase Shift	y=2+sin(4x)	$y = 2 + \sin (4 x)$
6038	Solve for w	0.7w=7(0.2w-0.9)	$0.7 w = 7 (0.2 w - 0.9)$
6039	Solve for y	(x-1)(x-1)(x-1)=y	$(x - 1) (x - 1) (x - 1) = y$
6040	Solve for b	(x+y)^7=x^7+7x^6y+ax^5y^2+35x^4y^b+35x^3y^4+21x^2y^5+7xy^6+y^7	${(x + y)}^{7} = x^{7} + 7 x^{6} y + a x^{5} y^{2} + 35 x^{4} y^{b} + 35 x^{3} y^{4} + 21 x^{2} y^{5} + 7 x y^{6} + y^{7}$
6041	Solve for x	105^(x+2)>1000	$105^{x + 2} > 1000$
6042	Find the Domain	y=(2x^3+3x)/(x^3-x^2-6x)	$y = \frac{2 x^{3} + 3 x}{x^{3} - x^{2} - 6 x}$
6043	Find All Complex Solutions	x^2+8x=-16	$x^{2} + 8 x = - 16$
6044	Find the Antiderivative	1/(x^2+x-2)	$\frac{1}{x^{2} + x - 2}$
6045	Simplify	5^-3*(5^7)/(5^-7)	$5^{- 3} \cdot \frac{5^{7}}{5^{- 7}}$
6046	Evaluate	(-3^-2)/(4^-1)	$\frac{- 3^{- 2}}{4^{- 1}}$
6047	Evaluate	(3m^-4)/(m^3)	$\frac{3 m^{- 4}}{m^{3}}$
6048	Solve for x	cube root of 14-10x=-2 cube root of x	$\sqrt[3]{14 - 10 x} = - 2 \sqrt[3]{x}$
6049	Multiply	(16x^2)/(36x^2-1)*(42x-7)/(14x^3)	$\frac{16 x^{2}}{36 x^{2} - 1} \cdot \frac{42 x - 7}{14 x^{3}}$
6050	Determine if Perpendicular	3x+2y=10 and 2x+3y=-3	$3 x + 2 y = 10$ and $2 x + 3 y = - 3$
6051	Find the End Behavior	f(x)=(x-2)^2(x+3)(x+1)^2	$f (x) = {(x - 2)}^{2} (x + 3) {(x + 1)}^{2}$
6052	Evaluate	1/2+(1/3)÷(1/2)-1/3	$\frac{1}{2} + \frac{1}{3} \div \frac{1}{2} - \frac{1}{3}$
6053	Simplify	i^85-9i^76-8i^85+5i^111	$i^{85} - 9 i^{76} - 8 i^{85} + 5 i^{111}$
6054	Solve for y	(3y)/5-8=-y	$\frac{3 y}{5} - 8 = - y$
6055	Multiply	(x-y)(x+y)(2x+y)	$(x - y) (x + y) (2 x + y)$
6056	Integrate Using u-Substitution	integral of (5-e^x)/(e^(2x)) with respect to x	$\int \frac{5 - e^{x}}{e^{2 x}} d x$
6057	Simplify the Radical Expression	y square root of 2x- square root of 8x^3+3 square root of 18x	$y \sqrt{2 x} - \sqrt{8 x^{3}} + 3 \sqrt{18 x}$
6058	Convert to Interval Notation	x^4+x^3-6x^2<=0	$x^{4} + x^{3} - 6 x^{2} \leq 0$
6059	Evaluate	8+2x-1=x-2-5x	$8 + 2 x - 1 = x - 2 - 5 x$
6060	Solve for x	Solve log of x=4	Solve $\log (x) = 4$
6061	Simplify	(3^(2/3)*5^(1/4))^6	${(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})}^{6}$
6062	Solve for a	(n root of a)^n=a	${(\sqrt[n]{a})}^{n} = a$
6063	Simplify	( square root of 2^5)/( cube root of 2)	$\frac{\sqrt{2^{5}}}{\sqrt[3]{2}}$
6064	Solve by Factoring	y^3-27=9y^2-27y	$y^{3} - 27 = 9 y^{2} - 27 y$
6065	Simplify	(y^3+5y^2)/(21y^3)*(9y^3)/(y+5)	$\frac{y^{3} + 5 y^{2}}{21 y^{3}} \cdot \frac{9 y^{3}}{y + 5}$
6066	Solve for w	25% of what number w is 9 ?	$25 %$ of what number $w$ is $9$ ?
6067	Simplify the Radical Expression	( fourth root of -y)^4	${(\sqrt[4]{- y})}^{4}$
6068	Simplify	(81^(1/2))/(9^(1/2))	$\frac{81^{\frac{1}{2}}}{9^{\frac{1}{2}}}$
6069	Simplify	25-9m^2-m+4m^3	$25 - 9 m^{2} - m + 4 m^{3}$
6070	Find the Inverse	y-2=7x	$y - 2 = 7 x$
6071	Evaluate	2(6(12-8)+7(17-9)+4)	$2 (6 (12 - 8) + 7 (17 - 9) + 4)$
6072	Solve the System of Equations	2r-t=7 r-t=1	$2 r - t = 7$ $r - t = 1$
6073	Simplify	(-8x^2y^8z^-5)/(12x^4y^-7z^7)	$\frac{- 8 x^{2} y^{8} z^{- 5}}{12 x^{4} y^{- 7} z^{7}}$
6074	Solve for k	3(2k-5)=6(k-4)+9	$3 (2 k - 5) = 6 (k - 4) + 9$
6075	Simplify	(2x^(1/6))^3x^2	${(2 x^{\frac{1}{6}})}^{3} x^{2}$
6076	Simplify	((3^6)/(12^6))^(-1/6)	${(\frac{3^{6}}{12^{6}})}^{- \frac{1}{6}}$
6077	Divide	(20 square root of 3)÷5 square root of 3	$20 \sqrt{3} \div 5 \sqrt{3}$
6078	Evaluate	(-10x^2+x)+(-2x^2+9x+7)	$(- 10 x^{2} + x) + (- 2 x^{2} + 9 x + 7)$
6079	Solve for y	square root of y-7=0	$\sqrt{y} - 7 = 0$
6080	Evaluate	log base 3 of 54- log base 3 of 8/15+ log base 3 of 4/5	$\log_{3} (54) - \log_{3} (\frac{8}{15}) + \log_{3} (\frac{4}{5})$
6081	Graph	y<-2/3x+3 y<3/2x	$y < - \frac{2}{3} x + 3$ $y < \frac{3}{2} x$
6082	Evaluate	square root of 10^-6	$\sqrt{10^{- 6}}$
6083	Simplify	square root of k^7 cube root of k^11	$\sqrt{k^{7}} \sqrt[3]{k^{11}}$
6084	Simplify	(54/64)^(1/3)	${(\frac{54}{64})}^{\frac{1}{3}}$
6085	Plot	y<x+3	$y < x + 3$
6086	Solve for y	(3y-6)/9=(4-2y)/-3	$\frac{3 y - 6}{9} = \frac{4 - 2 y}{- 3}$
6087	Solve for x	5x+8/3=7	$5 x + \frac{8}{3} = 7$
6088	Simplify	square root of p/(p^-3)	$\sqrt{\frac{p}{p^{- 3}}}$
6089	Find the Holes in the Graph	(x^2-3x-10)/(2x^2+3x-2)	$\frac{x^{2} - 3 x - 10}{2 x^{2} + 3 x - 2}$
6090	Solve for x	3 1/2>=1.4x	$3 \frac{1}{2} \geq 1.4 x$
6091	Simplify	(2^-3+3^-2)/(2^-2)	$\frac{2^{- 3} + 3^{- 2}}{2^{- 2}}$
6092	Solve for x	6^(3x^2-3x)=36^(15x-36)	$6^{3 x^{2} - 3 x} = 36^{15 x - 36}$
6093	Find the Exact Value	cos(175)cos(55)+sin(175)sin(55)	$\cos (175) \cdot \cos (55) + \sin (175) \cdot \sin (55)$
6094	Find the Domain and Range	f(x)=x^4+x^3-4x^2+5	$f (x) = x^{4} + x^{3} - 4 x^{2} + 5$
6095	Solve for x	4=(-5x+8)/(2x-6)	$4 = \frac{- 5 x + 8}{2 x - 6}$
6096	Solve the Rational Equation for x	4+ square root of x-2=x	$4 + \sqrt{x - 2} = x$
6097	Find the Exact Value	27 1/3-16 1/4-4 1/2	$27 \frac{1}{3} - 16 \frac{1}{4} - 4 \frac{1}{2}$
6098	Evaluate	18=6x+x(x-13)	$18 = 6 x + x (x - 13)$
6099	Solve the Inequality for x	square root of 6x-18+6<=15	$\sqrt{6 x - 18} + 6 \leq 15$
6100	Simplify	square root of 5( square root of 5+ square root of 2-3)	$\sqrt{5} (\sqrt{5} + \sqrt{2} - 3)$