Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
1901	Evaluate	(8*6!)/(3!)	$\frac{8 \cdot 6!}{3!}$
1902	Simplify the Radical Expression	square root of 18x^4y^6z^8	$\sqrt{18 x^{4} y^{6} z^{8}}$
1903	Solve for x	(2+x)/(7+x)=5/4	$\frac{2 + x}{7 + x} = \frac{5}{4}$
1904	Factor	3x^3-2y^3-6x^2y^2+xy	$3 x^{3} - 2 y^{3} - 6 x^{2} y^{2} + x y$
1905	Simplify	(5x^3y^2)/(3xy^0)	$\frac{5 x^{3} y^{2}}{3 x y^{0}}$
1906	Simplify	(a/b-b/a)/(1+b/a)	$\frac{\frac{a}{b} - \frac{b}{a}}{1 + \frac{b}{a}}$
1907	Find the Third Derivative	y=3x^-2+4x^-1+x	$y = 3 x^{- 2} + 4 x^{- 1} + x$
1908	Simplify	(16 cube root of 24)/(2 cube root of 3)	$\frac{16 \sqrt[3]{24}}{2 \sqrt[3]{3}}$
1909	Solve for x	12/18=(3x+4)/15	$\frac{12}{18} = \frac{3 x + 4}{15}$
1910	Simplify	(ax-ay)/(5x^2y^2)*(-(5xy)/(by-bx))	$\frac{a x - a y}{5 x^{2} y^{2}} \cdot (- \frac{5 x y}{b y - b x})$
1911	Factor	2a+ac^2-a^2c-2c	$2 a + a c^{2} - a^{2} c - 2 c$
1912	Find the Derivative - d/dx	d/(dx)((x^2+4)(2x^3+7x))	$\frac{d}{d x} ((x^{2} + 4) (2 x^{3} + 7 x))$
1913	Evaluate the Integral	integral of (4x^-2+6 square root of x-6/(x^2)) with respect to x	$\int (4 x^{- 2} + 6 \sqrt{x} - \frac{6}{x^{2}}) d x$
1914	Solve for x	7x+1=3x^2-2x+1	$7 x + 1 = 3 x^{2} - 2 x + 1$
1915	Simplify the Radical Expression	27 1/3	$27 \frac{1}{3}$
1916	Divide	((2x+3)/(8x^3+6x^2+x+15))	$(\frac{2 x + 3}{8 x^{3} + 6 x^{2} + x + 15})$
1917	Simplify	((10ab)^2(2a^4b^3))/(4a^5b)	$\frac{{(10 a b)}^{2} (2 a^{4} b^{3})}{4 a^{5} b}$
1918	Evaluate the Limit	limit as x approaches pi/2 of 2x-cos(x)	$lim_{x \to \frac{π}{2}} 2 x - \cos (x)$
1919	Expand Using the Binomial Theorem	(1/x+y)^5	${(\frac{1}{x} + y)}^{5}$
1920	Find the Integral	(-9x^2+10x)dx	$(- 9 x^{2} + 10 x) d x$
1921	Simplify	(-12t^-1u^5x^-4)/(2t^-3ux^5)	$\frac{- 12 t^{- 1} u^{5} x^{- 4}}{2 t^{- 3} u x^{5}}$
1922	Simplify	-5ab*(a^2-2b)	$- 5 a b \cdot (a^{2} - 2 b)$
1923	Find the Antiderivative	f(x)=sin(x)^2	$f (x) = \sin^{2} (x)$
1924	Simplify	((3r^-2s^3t^0)^-3)/(3rs)	$\frac{{(3 r^{- 2} s^{3} t^{0})}^{- 3}}{3 r s}$
1925	Find the Holes in the Graph	f(x)=(x^2-2x-3)/(x^2-9)	$f (x) = \frac{x^{2} - 2 x - 3}{x^{2} - 9}$
1926	Solve for x	10(x-1)-7x=x	$10 (x - 1) - 7 x = x$
1927	Divide Using Synthetic Division	(m^3-12m^2+33m)÷(m-5)	$(m^{3} - 12 m^{2} + 33 m) \div (m - 5)$
1928	Graph	3x-y^2=4x+25	$3 x - y^{2} = 4 x + 25$
1929	Solve the Inequality for m	1/4m<=-17	$\frac{1}{4} m \leq - 17$
1930	Simplify	(5a-b^3)(b^3+5a)	$(5 a - b^{3}) (b^{3} + 5 a)$
1931	Factor	(36a^2-64b^2)	$(36 a^{2} - 64 b^{2})$
1932	Find the Roots (Zeros)	256/2401	$\frac{256}{2401}$
1933	Solve for b	36^(3b)=216^(b+4)	$36^{3 b} = 216^{b + 4}$
1934	Simplify	(4((2-5)^3-4(1/2-5/3)^2)+3(2/6))- square root of 4	$(4 ({(2 - 5)}^{3} - 4 {(\frac{1}{2} - \frac{5}{3})}^{2}) + 3 (\frac{2}{6})) - \sqrt{4}$
1935	Solve for A	F-N=qA	$F - N = q A$
1936	Solve the Differential Equation	(y/x+ natural log of y)dx+(x/y+ natural log of x)dy=0	$(\frac{y}{x} + \ln (y)) d x + (\frac{x}{y} + \ln (x)) d y = 0$
1937	Simplify	3b^(1/2)*b^(3/2)	$3 b^{\frac{1}{2}} \cdot b^{\frac{3}{2}}$
1938	Simplify	(3x^-3y^2x^-4y^-4)/(3xy^23yx^-1)	$\frac{3 x^{- 3} y^{2} \cdot x^{- 4} y^{- 4}}{3 x y^{2} \cdot 3 y x^{- 1}}$
1939	Simplify	3^4x(3/(x^2))^-2	$3^{4} \cdot x \cdot {(\frac{3}{x^{2}})}^{- 2}$
1940	Simplify	((4r^2t)^3)^2	${({(4 r^{2} t)}^{3})}^{2}$
1941	Simplify	(-1 1/3p+6q)^2	${(- 1 \frac{1}{3} p + 6 q)}^{2}$
1942	Simplify	((4^(1/2))/(4^(3/4)))^4	${(\frac{4^{\frac{1}{2}}}{4^{\frac{3}{4}}})}^{4}$
1943	Graph	f(x)=f(x-1)+x^2+2x	$f (x) = f (x - 1) + x^{2} + 2 x$
1944	Simplify	(n root of a)^n	${(\sqrt[n]{a})}^{n}$
1945	Simplify	- square root of 4^4	$- \sqrt{4^{4}}$
1946	Simplify the Radical Expression	fourth root of (405x^3y^3)/(5x^-1y)	$\sqrt[4]{\frac{405 x^{3} y^{3}}{5 x^{- 1} y}}$
1947	Find the Asymptotes	y=x/(2-3x)	$y = \frac{x}{2 - 3 x}$
1948	Simplify	5 cube root of 3a+5 cube root of 3a-9 cube root of 3a	$5 \sqrt[3]{3 a} + 5 \sqrt[3]{3 a} - 9 \sqrt[3]{3 a}$
1949	Simplify the Radical Expression	6/(4+ square root of 5)	$\frac{6}{4 + \sqrt{5}}$
1950	Simplify	(3x^(-1/3)y^(3/4))^2	${(3 x^{- \frac{1}{3}} y^{\frac{3}{4}})}^{2}$
1951	Find the Domain and Range	f(x)=3/2 cube root of x+5	$f (x) = \frac{3}{2} \sqrt[3]{x} + 5$
1952	Evaluate the Integral	integral of x^2-x+x^-1 with respect to x	$\int x^{2} - x + x^{- 1} d x$
1953	Simplify	(6n^2+11n^3+2n)-(4n-3+5n^2)	$(6 n^{2} + 11 n^{3} + 2 n) - (4 n - 3 + 5 n^{2})$
1954	Solve for x	square root of x=1/2	$\sqrt{x} = \frac{1}{2}$
1955	Graph	x-y<-6 x-y<=1	$x - y < - 6$ $x - y \leq 1$
1956	Simplify the Radical Expression	square root of 3*2 square root of 2	$\sqrt{3} \cdot 2 \sqrt{2}$
1957	Find Amplitude, Period, and Phase Shift	y=cos((5x)/3-7/9)-10	$y = \cos (\frac{5 x}{3} - \frac{7}{9}) - 10$
1958	Simplify	3xy^2*(2xy+3y^2-cx^3)	$3 x y^{2} \cdot (2 x y + 3 y^{2} - c x^{3})$
1959	Simplify	((2x^-2y^3)/(3xy^-4))	$(\frac{2 x^{- 2} y^{3}}{3 x y^{- 4}})$
1960	Simplify	3 square root of 3+6 square root of 3-1/2 square root of 3	$3 \sqrt{3} + 6 \sqrt{3} - \frac{1}{2} \sqrt{3}$
1961	Simplify	(5 square root of 2a)/( square root of b^3)	$\frac{5 \sqrt{2 a}}{\sqrt{b^{3}}}$
1962	Write in Standard Form	-3x(5x+1)(8-2x)	$- 3 x (5 x + 1) (8 - 2 x)$
1963	Evaluate the Integral	integral from 0 to 2 of (x^3+1)^(1/2)x^2 with respect to x	$\int_{0}^{2} {(x^{3} + 1)}^{\frac{1}{2}} x^{2} d x$
1964	Solve for x	20/5=(4x)/6	$\frac{20}{5} = \frac{4 x}{6}$
1965	Graph	y>=-1/3x+3 y>3/4x-1	$y \geq - \frac{1}{3} x + 3$ $y > \frac{3}{4} x - 1$
1966	Simplify	((4s^5t^-7)/(-2s^-2t^4))	$(\frac{4 s^{5} t^{- 7}}{- 2 s^{- 2} t^{4}})$
1967	Simplify	((48^(1/4))/(6^(1/4)))^6	${(\frac{48^{\frac{1}{4}}}{6^{\frac{1}{4}}})}^{6}$
1968	Simplify	(a/b+1/a)(a-(a^3)/(a^2+b))	$(\frac{a}{b} + \frac{1}{a}) (a - \frac{a^{3}}{a^{2} + b})$
1969	Simplify	(5^(1/5))/5	$\frac{5^{\frac{1}{5}}}{5}$
1970	Simplify	(3+ square root of 5)/(1- square root of 5)	$\frac{3 + \sqrt{5}}{1 - \sqrt{5}}$
1971	Simplify	square root of x^5y^5*3 square root of 2x^7y^6	$\sqrt{x^{5} y^{5}} \cdot 3 \sqrt{2 x^{7} y^{6}}$
1972	Solve for y	1+4/y=11/(12y)	$1 + \frac{4}{y} = \frac{11}{12 y}$
1973	Simplify	(3^-2a^-1)/(9^-1b^-2c^0)	$\frac{3^{- 2} a^{- 1}}{9^{- 1} b^{- 2} c^{0}}$
1974	Expand Using Pascal's Triangle	(2x^3-y)^5	${(2 x^{3} - y)}^{5}$
1975	Simplify	5 cube root of a*4 square root of a^3	$5 \sqrt[3]{a} \cdot 4 \sqrt{a^{3}}$
1976	Simplify	-4a(1/2b+1/4c+1)	$- 4 a (\frac{1}{2} b + \frac{1}{4} c + 1)$
1977	Expand Using Sum/Difference Formulas	2x(5x-2)	$2 x (5 x - 2)$
1978	Simplify	3/(3^2)	$\frac{3}{3^{2}}$
1979	Find the x and y Intercepts	f(x)=x/2+1	$f (x) = \frac{x}{2} + 1$
1980	Solve the System of Equations	x-y=7 x-y=-4	$x - y = 7$ $x - y = - 4$
1981	Solve by Graphing	x-y=7 x-y=-4	$x - y = 7$ $x - y = - 4$
1982	Simplify	(3^2m^5t^6)/(3^5m^7t^-5)	$\frac{3^{2} m^{5} t^{6}}{3^{5} m^{7} t^{- 5}}$
1983	Solve for x	3(2x-3)<(-5)\|7-10\|	$3 (2 x - 3) < (- 5) \| 7 - 10 \|$
1984	Find the Intersection	y>1/2x-1 y<=-2x+6	$y > \frac{1}{2} x - 1$ $y \leq - 2 x + 6$
1985	Find the Antiderivative	f(x)=1/(3^x)	$f (x) = \frac{1}{3^{x}}$
1986	Rationalize the Denominator	(5x)/( cube root of x)	$\frac{5 x}{\sqrt[3]{x}}$
1987	Evaluate the Integral	integral of sin(x)^2cos(x)^3+2x with respect to x	$\int \sin^{2} (x) \cos^{3} (x) + 2 x d x$
1988	Solve for x	12=(x+1)(-3)	$12 = (x + 1) (- 3)$
1989	Simplify	( square root of 125- square root of 6)/( square root of 30-5)	$\frac{\sqrt{125} - \sqrt{6}}{\sqrt{30} - 5}$
1990	Simplify	( square root of 5+ square root of 2)/( square root of 8)	$\frac{\sqrt{5} + \sqrt{2}}{\sqrt{8}}$
1991	Find the Critical Points	f(x)=x^3+ax	$f (x) = x^{3} + a x$
1992	Simplify	(2 square root of 11-3)/( square root of 11+4)	$\frac{2 \sqrt{11} - 3}{\sqrt{11} + 4}$
1993	Find the Nth Root of the Given Value	n=4 , a=81	$n = 4$ , $a = 81$
1994	Solve for y	e^y=e^(2y)	$e^{y} = e^{2 y}$
1995	Solve the Inequality for t	-2t-5<9	$- 2 t - 5 < 9$
1996	Find the Roots (Zeros)	x^5+4x^3=0	$x^{5} + 4 x^{3} = 0$
1997	Write in Exponential Form	( square root of 5)^2	${(\sqrt{5})}^{2}$
1998	Evaluate the Integral	integral from 0 to 1 of 1/(1-x) with respect to x	$\int_{0}^{1} \frac{1}{1 - x} d x$
1999	Solve for x	log of x(x+6)=2	$\log (x) (x + 6) = 2$
2000	Find the Exact Value	18÷6+4÷2-15÷(-3)+4+(-2)÷(-1)	$18 \div 6 + 4 \div 2 - 15 \div (- 3) + 4 + (- 2) \div (- 1)$