Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
401	Solve for θ in Radians	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
402	Simplify the Radical Expression	fourth root of (k^16)/(16z^4)	$\sqrt[4]{\frac{k^{16}}{16 z^{4}}}$
403	Simplify	4/(y+2)-3/(y-2)+12/(y^2-4)	$\frac{4}{y + 2} - \frac{3}{y - 2} + \frac{12}{y^{2} - 4}$
404	Solve for x	(1/243)^(-x/3)=(1/9)^(-x/2+1)	${(\frac{1}{243})}^{- \frac{x}{3}} = {(\frac{1}{9})}^{- \frac{x}{2} + 1}$
405	Solve for x	log base 7 of 5x+3=3	$\log_{7} (5 x) + 3 = 3$
406	Write the Fraction in Simplest Form	( cube root of x^3)/( fifth root of x^2)	$\frac{\sqrt[3]{x^{3}}}{\sqrt[5]{x^{2}}}$
407	Simplify	(x^3+x^2y+xy^2+y^3)/(x^2+2xy+y^2)+(2xy)/(x+y)	$\frac{x^{3} + x^{2} y + x y^{2} + y^{3}}{x^{2} + 2 x y + y^{2}} + \frac{2 x y}{x + y}$
408	Simplify	(5p)/(2q-p)+(10q)/(p-2q)	$\frac{5 p}{2 q - p} + \frac{10 q}{p - 2 q}$
409	Find the Domain	(y^2+1)/(y^2-2y)	$\frac{y^{2} + 1}{y^{2} - 2 y}$
410	Evaluate	((4s^5t^-7)/(-2s^-2t^4))^3	${(\frac{4 s^{5} t^{- 7}}{- 2 s^{- 2} t^{4}})}^{3}$
411	Evaluate	5x^3=1080	$5 x^{3} = 1080$
412	Solve for s	2/5s=4 1/5	$\frac{2}{5} s = 4 \frac{1}{5}$
413	Simplify	fourth root of 256(5x-2)^12	$\sqrt[4]{256 {(5 x - 2)}^{12}}$
414	Simplify	3(m-4)-n(m-4)	$3 \cdot (m - 4) - n \cdot (m - 4)$
415	Simplify	3 fourth root of 27x^3*2 fourth root of 3x^5	$3 \sqrt[4]{27 x^{3}} \cdot 2 \sqrt[4]{3 x^{5}}$
416	Simplify	((2x^3)^2(3y^4)^3)/(12x^4y^5)	$\frac{{(2 x^{3})}^{2} {(3 y^{4})}^{3}}{12 x^{4} y^{5}}$
417	Solve for x	(0.3x^2-3x)(5x^3-0.2x^2)=0	$(0.3 x^{2} - 3 x) (5 x^{3} - 0.2 x^{2}) = 0$
418	Simplify	(-1/x)(1-x)/(1+x)x/(x^2-1)	$(- \frac{1}{x}) \cdot \frac{1 - x}{1 + x} \cdot \frac{x}{x^{2} - 1}$
419	Simplify	y+x-4+5x-1+y-3	$y + x - 4 + 5 x - 1 + y - 3$
420	Simplify	(2x-7y)/(2x^2y)-(5y-8x)/(5xy^2)	$\frac{2 x - 7 y}{2 x^{2} y} - \frac{5 y - 8 x}{5 x y^{2}}$
421	Solve for x	2 1/3(2x-3)=2 1/3	$2 \frac{1}{3} (2 x - 3) = 2 \frac{1}{3}$
422	Find the Product	((x+1)-y)^3	${((x + 1) - y)}^{3}$
423	Simplify	(-2)^-3-24	${(- 2)}^{- 3} - 24$
424	Solve for k	k=1+ square root of 3k-5	$k = 1 + \sqrt{3 k - 5}$
425	Solve for x	3 2/7x=12/35	$3 \frac{2}{7} x = \frac{12}{35}$
426	Simplify	(x+1)(x+2)(y-3)	$(x + 1) (x + 2) (y - 3)$
427	Find the Asymptotes	f(x)=(7+3e^(3x))/(4-8e^(3x))	$f (x) = \frac{7 + 3 e^{3 x}}{4 - 8 e^{3 x}}$
428	Simplify	((2x^0)/(4x^-2y^4))^2	${(\frac{2 x^{0}}{4 x^{- 2} y^{4}})}^{2}$
429	Simplify	square root of cube root of 125	$\sqrt{\sqrt[3]{125}}$
430	Evaluate the Limit	limit as w approaches 5 of (2w^4-9w^3+19)^(-1/2)	$lim_{w \to 5} {(2 w^{4} - 9 w^{3} + 19)}^{- \frac{1}{2}}$
431	Simplify	4r^-7s^-1*7r^-2s^5t^0	$4 r^{- 7} s^{- 1} \cdot 7 r^{- 2} s^{5} t^{0}$
432	Simplify	2/(-4x+4 square root of 5x)	$\frac{2}{- 4 x + 4 \sqrt{5 x}}$
433	Convert to Radical Form	(x+y)^(1/3)	${(x + y)}^{\frac{1}{3}}$
434	Solve for x	2 square root of 3x+1=4x	$2 \sqrt{3 x + 1} = 4 x$
435	Evaluate the Integral	integral from 1 to 2 of (3x^2+4x^3) with respect to x	$\int_{1}^{2} (3 x^{2} + 4 x^{3}) d x$
436	Simplify	6 cube root of 25ab^2*5 cube root of 5a^2b	$6 \sqrt[3]{25 a b^{2}} \cdot 5 \sqrt[3]{5 a^{2} b}$
437	Simplify	(-4x+2x^3-5)+(6x^2-3x+6x^3)+(13-2x^2+9x-8x^2)	$(- 4 x + 2 x^{3} - 5) + (6 x^{2} - 3 x + 6 x^{3}) + (13 - 2 x^{2} + 9 x - 8 x^{2})$
438	Simplify	16/(x-4)-(x^2)/(x-4)	$\frac{16}{x - 4} - \frac{x^{2}}{x - 4}$
439	Solve for p	p^2+p-90=0	$p^{2} + p - 90 = 0$
440	Simplify	fourth root of (x^8)/(y^4)	$\sqrt[4]{\frac{x^{8}}{y^{4}}}$
441	Solve for x	square root of (x-10)^2=x-10	$\sqrt{{(x - 10)}^{2}} = x - 10$
442	Simplify	(b-c)/(a+b)-(ab-b^2)/(a^2-ac)*(a^2-c^2)/(a^2-b^2)	$\frac{b - c}{a + b} - \frac{a b - b^{2}}{a^{2} - a c} \cdot \frac{a^{2} - c^{2}}{a^{2} - b^{2}}$
443	Simplify	square root of fourth root of 8^10	$\sqrt{\sqrt[4]{8^{10}}}$
444	Simplify	(24a^5b^2)/((2ab)^4)	$\frac{24 a^{5} b^{2}}{{(2 a b)}^{4}}$
445	Solve for x	x+ square root of x^2+3=3x	$x + \sqrt{x^{2} + 3} = 3 x$
446	Solve for θ	cos(theta)+sin(theta)*tan(theta)=2	$\cos (θ) + \sin (θ) \cdot \tan (θ) = 2$
447	Verify the Identity	1-cos(x)^2=(cos(x)sin(x))/(cot(x))	$1 - \cos^{2} (x) = \frac{\cos (x) \sin (x)}{\cot (x)}$
448	Simplify	b/((a-b)^2)-(a+b)/(b^2-ab)	$\frac{b}{{(a - b)}^{2}} - \frac{a + b}{b^{2} - a b}$
449	Find the Inverse	f(x)=4x^2 , x<=0	$f (x) = 4 x^{2}$ , $x \leq 0$
450	Evaluate	(-16-8)/2+25÷5+1	$\frac{- 16 - 8}{2} + 25 \div 5 + 1$
451	Solve the Differential Equation	xy'=x^2sin(x)+y	$x y' = x^{2} \sin (x) + y$
452	Simplify	2a^2b-5/2ab^2+7/12ab^2+5/6a^2b	$2 a^{2} b - \frac{5}{2} a b^{2} + \frac{7}{12} a b^{2} + \frac{5}{6} a^{2} b$
453	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 25x^2-7)/(x+2)	$lim_{x \to - \infty} \frac{\sqrt{25 x^{2} - 7}}{x + 2}$
454	Simplify	(sin(theta)^4-cos(theta)^4)/(sin(theta)cos(theta))	$\frac{\sin^{4} (θ) - \cos^{4} (θ)}{\sin (θ) \cos (θ)}$
455	Simplify	((x^2-bx+ax-ab)/(x^2+bx-ax-ab))÷((x^2+bx+ax+ab)/(x^2-bx-ax+ab))	$\frac{x^{2} - b x + a x - a b}{x^{2} + b x - a x - a b} \div \frac{x^{2} + b x + a x + a b}{x^{2} - b x - a x + a b}$
456	Simplify	(x^-3)(3x^-2)^-1	$(x^{- 3}) {(3 x^{- 2})}^{- 1}$
457	Solve for x	2 3/5x=9/15	$2 \frac{3}{5} x = \frac{9}{15}$
458	Evaluate	3x-4(2+x)=18	$3 x - 4 (2 + x) = 18$
459	Find the Domain	(4y)/(3x^2+2xy)-(9x)/(3xy+2y^2)	$\frac{4 y}{3 x^{2} + 2 x y} - \frac{9 x}{3 x y + 2 y^{2}}$
460	Simplify	12m+5-7d+3+6m-1+8d	$12 m + 5 - 7 d + 3 + 6 m - 1 + 8 d$
461	Find the Antiderivative	x^2+2/(x^2)	$x^{2} + \frac{2}{x^{2}}$
462	Simplify	((2x^-3y^-2)^5)/((6x^-1y^-8)^2)	$\frac{{(2 x^{- 3} y^{- 2})}^{5}}{{(6 x^{- 1} y^{- 8})}^{2}}$
463	Solve for x	(x+ square root of 3)^2-(x- square root of 3)^2=8 square root of 3	${(x + \sqrt{3})}^{2} - {(x - \sqrt{3})}^{2} = 8 \sqrt{3}$
464	Simplify	(ab^2-a^2b)/(ab)*(a^2b^2)/(a-b)	$\frac{a b^{2} - a^{2} b}{a b} \cdot \frac{a^{2} b^{2}}{a - b}$
465	Simplify	(49^(3/8)*49^(7/8))/(7^(5/4))	$\frac{49^{\frac{3}{8}} \cdot 49^{\frac{7}{8}}}{7^{\frac{5}{4}}}$
466	Graph	g(x)=F(x)-3	$g (x) = F (x) - 3$
467	Simplify	(- square root of 36)/( square root of 64)	$\frac{- \sqrt{36}}{\sqrt{64}}$
468	Simplify	((3-4i)/5)^-1	${(\frac{3 - 4 i}{5})}^{- 1}$
469	Simplify	7a^4b*(-3a^5b^6)^2	$7 a^{4} b \cdot {(- 3 a^{5} b^{6})}^{2}$
470	Simplify	(3 square root of 3)/( square root of 6m)	$\frac{3 \sqrt{3}}{\sqrt{6 m}}$
471	Graph	y< = square root of 2x+4-3	$y \leq \sqrt{2 x + 4} - 3$
472	Simplify the Radical Expression	fourth root of 6* fourth root of 8	$\sqrt[4]{6} \cdot \sqrt[4]{8}$
473	Find the Antiderivative	f(x)=2x-3x^2	$f (x) = 2 x - 3 x^{2}$
474	Factor	a^3x^2-16a^3x+64a^3-b^3x^2+16b^3x-64b^3	$a^{3} x^{2} - 16 a^{3} x + 64 a^{3} - b^{3} x^{2} + 16 b^{3} x - 64 b^{3}$
475	Solve for x	4x-2*(3x-2)=3x	$4 x - 2 \cdot (3 x - 2) = 3 x$
476	Evaluate	(z^8*z^2)/(z^5)	$\frac{z^{8} \cdot z^{2}}{z^{5}}$
477	Find the Axis of Symmetry	x=-1/2y^2-4y-7	$x = - \frac{1}{2} y^{2} - 4 y - 7$
478	Solve for x	square root of 4x^2-20x+25=5-2x	$\sqrt{4 x^{2} - 20 x + 25} = 5 - 2 x$
479	Solve for x	x^3=3x^2	$x^{3} = 3 x^{2}$
480	Simplify	8*(-1/2x^3y)^2-3y^5-x^6y^2	$8 \cdot {(- \frac{1}{2} x^{3} y)}^{2} - 3 y^{5} - x^{6} y^{2}$
481	Find the Product	(2+(x-1))(2-(x-1))	$(2 + (x - 1)) (2 - (x - 1))$
482	Simplify	( square root of 12)/( fourth root of 3)	$\frac{\sqrt{12}}{\sqrt[4]{3}}$
483	Find the Integral	x(x^2+9)^(1/2)	$x {(x^{2} + 9)}^{\frac{1}{2}}$
484	Evaluate	1/4(4)^(3/2)	$\frac{1}{4} {(4)}^{\frac{3}{2}}$
485	Factor	8x^5-25y^3+80x^4-x^2y^3+200x^3-10xy^3	$8 x^{5} - 25 y^{3} + 80 x^{4} - x^{2} y^{3} + 200 x^{3} - 10 x y^{3}$
486	Solve for x	5(x-a)=3(x+b)	$5 (x - a) = 3 (x + b)$
487	Evaluate	(1/(2r^6))^-6	${(\frac{1}{2 r^{6}})}^{- 6}$
488	Simplify	((a+b)/b-a/(a+b))÷((a+b)/a-b/(a+b))	$(\frac{a + b}{b} - \frac{a}{a + b}) \div (\frac{a + b}{a} - \frac{b}{a + b})$
489	Solve Using the Quadratic Formula	x^4+12x^2-8	$x^{4} + 12 x^{2} - 8$
490	Solve for x	-7/9(x+3)=14	$- \frac{7}{9} (x + 3) = 14$
491	Simplify the Radical Expression	(x^2y^8)^(2/3)	${(x^{2} y^{8})}^{\frac{2}{3}}$
492	Simplify	(2 2/9a^(3m-2/3))^3*(0.45a^(m-5))^3	${(2 \frac{2}{9} a^{3 m - \frac{2}{3}})}^{3} \cdot {(0.45 a^{m - 5})}^{3}$
493	Simplify the Radical Expression	1/(2+ square root of 5)	$\frac{1}{2 + \sqrt{5}}$
494	Simplify	121÷11+(3*4)÷2	$121 \div 11 + 3 \cdot 4 \div 2$
495	Simplify the Radical Expression	sixth root of (g^6h)/(h^7)	$\sqrt[6]{\frac{g^{6} h}{h^{7}}}$
496	Solve for x	8- square root of x+12=3	$8 - \sqrt{x + 12} = 3$
497	Solve for u	m/(u^2)+r=-k-y	$\frac{m}{u^{2}} + r = - k - y$
498	Find the Domain	(ab^2-a^2b)/(ab)*(a^2b^2)/(a-b)	$\frac{a b^{2} - a^{2} b}{a b} \cdot \frac{a^{2} b^{2}}{a - b}$
499	Solve for x	(x-2 square root of 5)(x+5 square root of 2)=x^2-10 square root of 10	$(x - 2 \sqrt{5}) (x + 5 \sqrt{2}) = x^{2} - 10 \sqrt{10}$
500	Solve for x	6x^3(2x+4)=2x(6x^3+12x^2-10)+60	$6 x^{3} (2 x + 4) = 2 x (6 x^{3} + 12 x^{2} - 10) + 60$