Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
4501	Simplify	1/(a^2+ab)+1/(ab+b^2)	$\frac{1}{a^{2} + a b} + \frac{1}{a b + b^{2}}$
4502	Simplify	5((5^3)/(2/5))^2	$5 {(\frac{5^{3}}{\frac{2}{5}})}^{2}$
4503	Determine if Odd, Even, or Neither	f(x)=e^(x^8-x)	$f (x) = e^{x^{8} - x}$
4504	Find the Derivative - d/dx	(x+2)^5(x-3)^4	${(x + 2)}^{5} {(x - 3)}^{4}$
4505	Simplify	6 cube root of -2	$6 \sqrt[3]{- 2}$
4506	Evaluate the Limit	limit as x approaches 4 of (2 square root of x-2)/(2x-4)	$lim_{x \to 4} \frac{2 \sqrt{x} - 2}{2 x - 4}$
4507	Simplify	8a^-3b^2c^-2	$8 a^{- 3} b^{2} c^{- 2}$
4508	Evaluate	(-1)^4(-3)^-39^2	${(- 1)}^{4} \cdot {(- 3)}^{- 3} \cdot 9^{2}$
4509	Solve for x	x-2 = square root of x-2+12	$x - 2 = \sqrt{x - 2} + 12$
4510	Find the Antiderivative	2sin(x)+x^2	$2 \sin (x) + x^{2}$
4511	Rationalize the Denominator	( square root of 6+18)/(2 square root of 3)	$\frac{\sqrt{6} + 18}{2 \sqrt{3}}$
4512	Find the Integral	(4e^2)/(x^-3)	$\frac{4 e^{2}}{x^{- 3}}$
4513	Solve for h	2(3h+9)=3(-2h+10)	$2 (3 h + 9) = 3 (- 2 h + 10)$
4514	Simplify	(2x*3x^5)^3	${(2 x \cdot 3 x^{5})}^{3}$
4515	Solve for y	y=2-9x , x=2/3	$y = 2 - 9 x$ , $x = \frac{2}{3}$
4516	Simplify	((4a^-1b^-4)^-3)/((-8a^4b^-2)^-2)	$\frac{{(4 a^{- 1} b^{- 4})}^{- 3}}{{(- 8 a^{4} b^{- 2})}^{- 2}}$
4517	Solve for x	3/(x-1)=x+1	$\frac{3}{x - 1} = x + 1$
4518	Solve for x	1/(x+5)+x/(5-x)=(2x)/(x^2-25)	$\frac{1}{x + 5} + \frac{x}{5 - x} = \frac{2 x}{x^{2} - 25}$
4519	Simplify	( square root of 5a)( square root of 2a)(3 square root of 10a^2)	$(\sqrt{5 a}) (\sqrt{2 a}) (3 \sqrt{10 a^{2}})$
4520	Simplify	((4x^(1/4)y^2)/(xy^(1/5)))^(1/2)	${(\frac{4 x^{\frac{1}{4}} y^{2}}{x y^{\frac{1}{5}}})}^{\frac{1}{2}}$
4521	Simplify the Radical Expression	2 square root of 18-2 square root of 12+2 square root of 18	$2 \sqrt{18} - 2 \sqrt{12} + 2 \sqrt{18}$
4522	Solve for j	8/j=j/2	$\frac{8}{j} = \frac{j}{2}$
4523	Evaluate	-2cos(theta)^2+sin(theta)+1=0	$- 2 \cos^{2} (θ) + \sin (θ) + 1 = 0$
4524	Solve for b	10 = square root of b/9+10	$10 = \sqrt{\frac{b}{9}} + 10$
4525	Multiply	square root of 9* square root of 4	$\sqrt{9} \cdot \sqrt{4}$
4526	Solve the Inequality for r	r-(-5)>-2	$r - (- 5) > - 2$
4527	Simplify the Radical Expression	45^(-3/2)*45^2	$45^{- \frac{3}{2}} \cdot 45^{2}$
4528	Find the Focus	y^2=4x+4	$y^{2} = 4 x + 4$
4529	Find the Reference Angle	sin(510 degrees )	$\sin (510 °)$
4530	Simplify	21 root of c^-3*c^-4	$\sqrt[21]{c^{- 3} \cdot c^{- 4}}$
4531	Solve for x	6^(-2x^2+4x)=(1/36)^(6x+20)	$6^{- 2 x^{2} + 4 x} = {(\frac{1}{36})}^{6 x + 20}$
4532	Rationalize the Denominator	(4x cube root of 6)/(5 cube root of 9x)	$\frac{4 x \sqrt[3]{6}}{5 \sqrt[3]{9 x}}$
4533	Divide	(11x^5+7x^3-2x)/(x^2)	$\frac{11 x^{5} + 7 x^{3} - 2 x}{x^{2}}$
4534	Solve for x	3x^(1/3)+3=5	$3 x^{\frac{1}{3}} + 3 = 5$
4535	Factor	14a^5n^4p-28a^6n	$14 a^{5} n^{4} p - 28 a^{6} n$
4536	Find the End Behavior	f(x)=70+14x^2+59x+x^3	$f (x) = 70 + 14 x^{2} + 59 x + x^{3}$
4537	Simplify	4x cube root of 64x^5	$4 x \sqrt[3]{64 x^{5}}$
4538	Find the Exact Value	(2 4/9-5 2/3)/2 1/3	$\frac{2 \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$
4539	Graph	y<-2x+1 y>=-1/3x+3	$y < - 2 x + 1$ $y \geq - \frac{1}{3} x + 3$
4540	Solve for a	-5/6=a-2/3	$- \frac{5}{6} = a - \frac{2}{3}$
4541	Expand the Logarithmic Expression	log base 7 of (1/2m^5)^4	$\log_{7} ({(\frac{1}{2} m^{5})}^{4})$
4542	Rationalize the Denominator	( cube root of 10)÷( cube root of 2)	$\sqrt[3]{10} \div \sqrt[3]{2}$
4543	Find the Second Derivative	y=xcos(5x)-sin(x)^2	$y = x \cos (5 x) - \sin^{2} (x)$
4544	Simplify	3^0*2^-3(100x^2)^0	$3^{0} \cdot 2^{- 3} {(100 x^{2})}^{0}$
4545	Evaluate	(4^3-2^5)/(2^3)	$\frac{4^{3} - 2^{5}}{2^{3}}$
4546	Simplify the Radical Expression	4 square root of 36x^2y^3z^4	$4 \sqrt{36 x^{2} y^{3} z^{4}}$
4547	Solve for x	3x^(4/3)+5=53	$3 x^{\frac{4}{3}} + 5 = 53$
4548	Simplify	b/(2a^2-ab)-(4a)/(2ab-b^2)	$\frac{b}{2 a^{2} - a b} - \frac{4 a}{2 a b - b^{2}}$
4549	Solve the System of Equations	y=x^2-5x+8 y=-2x^2-13	$y = x^{2} - 5 x + 8$ $y = - 2 x^{2} - 13$
4550	Write as a Single Logarithm	1/2( log base 6 of k^9- log base 6 of k^3)	$\frac{1}{2} (\log_{6} (k^{9}) - \log_{6} (k^{3}))$
4551	Simplify	((m^2n^(1/2))^0)/(n^(3/4))	$\frac{{(m^{2} n^{\frac{1}{2}})}^{0}}{n^{\frac{3}{4}}}$
4552	Solve the System of Equations	y=x^2-2x+4 y=-x^2-2x+4	$y = x^{2} - 2 x + 4$ $y = - x^{2} - 2 x + 4$
4553	Simplify	a(a+9b)^2	$a {(a + 9 b)}^{2}$
4554	Write in Slope-Intercept Form	y-5/2=-2(x+1)	$y - \frac{5}{2} = - 2 (x + 1)$
4555	Graph	8x>=-24 and 10>2x+6	$8 x \geq - 24$ and $10 > 2 x + 6$
4556	Solve for x	(1/243)^(2x-14)=243^(-x+8)	${(\frac{1}{243})}^{2 x - 14} = 243^{- x + 8}$
4557	Find the Domain and Range	4x=-3y+xy	$4 x = - 3 y + x y$
4558	Graph	9x^0y^(-)*3	$9 x^{0} y^{-} \cdot 3$
4559	Simplify	((3x)/16)÷((3x-9)/20)	$\frac{3 x}{16} \div \frac{3 x - 9}{20}$
4560	Simplify	3xy(x^2+xy+y^2)	$3 x y (x^{2} + x y + y^{2})$
4561	Solve for x	2 square root of 4x-1=-1	$2 \sqrt{4 x - 1} = - 1$
4562	Evaluate	1/3x^4=27	$\frac{1}{3} x^{4} = 27$
4563	Solve for y	6 square root of y-5=y+3	$6 \sqrt{y - 5} = y + 3$
4564	Solve for q	x^2+px+q=(x-13)(x+1)	$x^{2} + p x + q = (x - 13) (x + 1)$
4565	Solve by Addition/Elimination	2x+3y=6 2y=5-x	$2 x + 3 y = 6$ $2 y = 5 - x$
4566	Find Amplitude, Period, and Phase Shift	y=-4sin(x+6pi)-8	$y = - 4 \sin (x + 6 π) - 8$
4567	Evaluate the Limit	limit as x approaches 0 of (1/x)^x	$lim_{x \to 0} {(\frac{1}{x})}^{x}$
4568	Simplify	(x+3y-6z)^2	${(x + 3 y - 6 z)}^{2}$
4569	Solve by Substitution	8x-3y=10 8x^2-3y^2+30y=80	$8 x - 3 y = 10$ $8 x^{2} - 3 y^{2} + 30 y = 80$
4570	Solve for m	8(4-5m)=-4(6+8m)	$8 (4 - 5 m) = - 4 (6 + 8 m)$
4571	Simplify	(x+6)/2-3x	$\frac{x + 6}{2} - 3 x$
4572	Graph	{(x,y)\|x=2}	${(x, y) \| x = 2}$
4573	Find the Quadratic Equation Given the Roots	-2 , 1+ square root of 7	$- 2$ , $1 + \sqrt{7}$
4574	Find the Third Derivative	y=ax^4+bx^2+c	$y = a x^{4} + b x^{2} + c$
4575	Find the Roots (Zeros)	0=x^2(x+3)^2(x-1)	$0 = x^{2} {(x + 3)}^{2} (x - 1)$
4576	Simplify	(5/8-1/3)÷(2/5+1)	$(\frac{5}{8} - \frac{1}{3}) \div (\frac{2}{5} + 1)$
4577	Solve for x	20=20 log of x/200	$20 = 20 \log (\frac{x}{200})$
4578	Simplify	5b^2+(a^2+5b)(ab-b^2)	$5 b^{2} + (a^{2} + 5 b) (a b - b^{2})$
4579	Write in Exponential Form	( square root of x)^2	${(\sqrt{x})}^{2}$
4580	Find the Antiderivative	2x^(2/3)-5x^3	$2 x^{\frac{2}{3}} - 5 x^{3}$
4581	Evaluate the Integral	integral of 4/(x^3)-5x square root of x with respect to x	$\int \frac{4}{x^{3}} - 5 x \sqrt{x} d x$
4582	Simplify	(3/4)÷(12/(2x+6))	$\frac{3}{4} \div \frac{12}{2 x + 6}$
4583	Solve by Factoring	5w^3=50w	$5 w^{3} = 50 w$
4584	Solve the System of Equations	y=x+4 2x-2y=10	$y = x + 4$ $2 x - 2 y = 10$
4585	Find All Complex Solutions	square root of 9x+10=x	$\sqrt{9 x + 10} = x$
4586	Solve by Graphing	y=-3/5x-1 y=-4/5x	$y = - \frac{3}{5} x - 1$ $y = - \frac{4}{5} x$
4587	Simplify	(4x^3(x^2-4)^(5/3))/((2x)^3(x-2) cube root of (x^2-4)^2)	$\frac{4 x^{3} {(x^{2} - 4)}^{\frac{5}{3}}}{{(2 x)}^{3} (x - 2) \sqrt[3]{{(x^{2} - 4)}^{2}}}$
4588	Simplify	(2 square root of x-3 square root of y)/( square root of x+ square root of y)	$\frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}}$
4589	Find the Product	-2(3x^2-x-5)	$- 2 (3 x^{2} - x - 5)$
4590	Solve for x	cube root of 2x-1+3=0	$\sqrt[3]{2 x - 1} + 3 = 0$
4591	Graph	x>=4 y<=x-3	$x \geq 4$ $y \leq x - 3$
4592	Graph	yy<=-1/2x+1	$y \cdot y \leq - \frac{1}{2} x + 1$
4593	Simplify	3/4c-7/12+7/24c+2/3-1/6c	$\frac{3}{4} c - \frac{7}{12} + \frac{7}{24} c + \frac{2}{3} - \frac{1}{6} c$
4594	Graph	x<y+3	$x < y + 3$
4595	Solve the Function Operation	f(n)=2n+1 g(n)=3n Find f(n)+g(n)	$f (n) = 2 n + 1$ $g (n) = 3 n$ Find $f (n) + g (n)$
4596	Simplify	3 fourth root of 8*7 fourth root of 32	$3 \sqrt[4]{8} \cdot 7 \sqrt[4]{32}$
4597	Write in Standard Form	y=(x+4)(x+1)(x-1)^2	$y = (x + 4) (x + 1) {(x - 1)}^{2}$
4598	Solve by Addition/Elimination	3x+6y=27 x+2y=11	$3 x + 6 y = 27$ $x + 2 y = 11$
4599	Solve Using the Quadratic Formula	mg=w	$mg = w$
4600	Simplify	8/(2s^-3)	$\frac{8}{2 s^{- 3}}$