Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
202101	Simplify	(( square root of 6-i square root of 3)/3)(( square root of 6+i square root of 3)/3)	$(\frac{\sqrt{6} - i \sqrt{3}}{3}) (\frac{\sqrt{6} + i \sqrt{3}}{3})$
202102	Find the Exact Value	(-2)^-3-24	${(- 2)}^{- 3} - 24$
202103	Simplify	(8a^3-1/27)/((2a-1/3)^2)	$\frac{8 a^{3} - \frac{1}{27}}{{(2 a - \frac{1}{3})}^{2}}$
202104	Combine Like Terms	(-6x^2-3x-1)-(x+8)	$(- 6 x^{2} - 3 x - 1) - (x + 8)$
202105	Simplify the Radical Expression	x^2 square root of 75- square root of 12x^4	$x^{2} \sqrt{75} - \sqrt{12 x^{4}}$
202106	Graph	x^2+(y-3 square root of x^2)^2=1	$x^{2} + {(y - 3 \sqrt{x^{2}})}^{2} = 1$
202107	Solve for x	square root of x=3 square root of 7	$\sqrt{x} = 3 \sqrt{7}$
202108	Solve the Inequality for x	x^2+3<=4x	$x^{2} + 3 \leq 4 x$
202109	Solve for b	(2x+1)/((x+2)(x-3))=a/(x+2)+b/(x-3)	$\frac{2 x + 1}{(x + 2) (x - 3)} = \frac{a}{x + 2} + \frac{b}{x - 3}$
202110	Find the x and y Intercepts	y=-(x+3)(x+1)^2(2x-5)	$y = - (x + 3) {(x + 1)}^{2} (2 x - 5)$
202111	Multiply	(1+i)(2+i)	$(1 + i) (2 + i)$
202112	Simplify	(tan(theta)^2-sec(theta)^2)(sin(theta)^2+cos(theta)^2)	$(\tan^{2} (θ) - \sec^{2} (θ)) (\sin^{2} (θ) + \cos^{2} (θ))$
202113	Solve the Inequality for w	7w>-49	$7 w > - 49$
202114	Multiply	(4-x)(2x+7)	$(4 - x) (2 x + 7)$
202115	Solve for h	square root of 3h=3	$\sqrt{3 h} = 3$
202116	Find the Domain and Range	f(x)=(6x)^(1/2)+3	$f (x) = {(6 x)}^{\frac{1}{2}} + 3$
202117	Evaluate	1/(2^3-5)	$\frac{1}{2^{3} - 5}$
202118	Simplify	(x^3-y^3)/(x+y)*(x^2-y^2)/(x^2+xy+y^2)	$\frac{x^{3} - y^{3}}{x + y} \cdot \frac{x^{2} - y^{2}}{x^{2} + x y + y^{2}}$
202119	Graph	F(x)=e^(x+2)	$F (x) = e^{x + 2}$
202120	Solve for x	(5(x-8))/6=-7	$\frac{5 (x - 8)}{6} = - 7$
202121	Convert to a Decimal	14rad	$14$ radians
202122	Simplify the Radical Expression	fourth root of (3a^2)/(8b^3)	$\sqrt[4]{\frac{3 a^{2}}{8 b^{3}}}$
202123	Solve for x	10x+2x-100-100=2x+8x+300+200	$10 x + 2 x - 100 - 100 = 2 x + 8 x + 300 + 200$
202124	Write as a Single Logarithm	log base 3 of a^7+( log base 3 of a^4-2* log base 3 of b)	$\log_{3} (a^{7}) + (\log_{3} (a^{4}) - 2 \cdot \log_{3} (b))$
202125	Solve for d	1/4(d-3)=-15	$\frac{1}{4} (d - 3) = - 15$
202126	Find the Exact Value	2sin(pi/3)-3tan(pi/6)	$2 \sin (\frac{π}{3}) - 3 \tan (\frac{π}{6})$
202127	Simplify the Radical Expression	(-64)^(-1/3)	${(- 64)}^{- \frac{1}{3}}$
202128	Simplify	( square root of 2x)/(3- square root of 2x)	$\frac{\sqrt{2 x}}{3 - \sqrt{2 x}}$
202129	Find the Domain and Range	f(x)=1/4 cube root of x+2-5	$f (x) = \frac{1}{4} \sqrt[3]{x + 2} - 5$
202130	Find the Domain and Range	y=2(3)^(x-1)+4	$y = 2 {(3)}^{x - 1} + 4$
202131	Simplify	(2x)/(3x-18)+(x+1)/(x-6)	$\frac{2 x}{3 x - 18} + \frac{x + 1}{x - 6}$
202132	Simplify	square root of cube root of 64	$\sqrt[2]{\sqrt[3]{64}}$
202133	Simplify	x^-3y^-2z	$x^{- 3} y^{- 2} z$
202134	Simplify	2n+5.5-0.9n-8+4.5p	$2 n + 5.5 - 0.9 n - 8 + 4.5 p$
202135	Write in Standard Form	(4+2n^3)+(5n^3+2)	$(4 + 2 n^{3}) + (5 n^{3} + 2)$
202136	Solve for x	5x-(x+3)=1/3(9x+18)-5	$5 x - (x + 3) = \frac{1}{3} (9 x + 18) - 5$
202137	Simplify	fourth root of 6*3 fourth root of 6	$\sqrt[4]{6} \cdot 3 \sqrt[4]{6}$
202138	Simplify	(5 fourth root of 2)/(4 fourth root of 162)	$\frac{5 \sqrt[4]{2}}{4 \sqrt[4]{162}}$
202139	Simplify the Radical Expression	ninth root of 27	$\sqrt[9]{27}$
202140	Solve for m	m/3=(m^2)/6	$\frac{m}{3} = \frac{m^{2}}{6}$
202141	Simplify	28 root of 1/(p^6*p)	$\sqrt[28]{\frac{1}{p^{6} \cdot p}}$
202142	Simplify	(x^2y^2)/(y^2)	$\frac{x^{2} y^{2}}{y^{2}}$
202143	Subtract	9/12-3/6	$\frac{9}{12} - \frac{3}{6}$
202144	Simplify	(tan(theta)+cos(theta)csc(theta))/(sec(theta)csc(theta))	$\frac{\tan (θ) + \cos (θ) \csc (θ)}{\sec (θ) \csc (θ)}$
202145	Simplify the Radical Expression	4/( fourth root of 8m^2)	$\frac{4}{\sqrt[4]{8 m^{2}}}$
202146	Simplify	(x^(-1/3))^(-1/6)	${(x^{- \frac{1}{3}})}^{- \frac{1}{6}}$
202147	Simplify	((x+1) square root of x-2)/( square root of x^2-x-2)	$\frac{(x + 1) \sqrt{x - 2}}{\sqrt{x^{2} - x - 2}}$
202148	Simplify	(3 cube root of 32m^2)/( cube root of 4m)	$\frac{3 \sqrt[3]{32 m^{2}}}{\sqrt[3]{4 m}}$
202149	Find f(g(x))	f(x)=x^3+12x^2+25x-70 g(x)=x+7	$f (x) = x^{3} + 12 x^{2} + 25 x - 70$ $g (x) = x + 7$
202150	Graph	y>=3 y<=x y<=-1/2x+8	$y \geq 3$ $y \leq x$ $y \leq - \frac{1}{2} x + 8$
202151	Simplify the Radical Expression	fourth root of 1/32	$\sqrt[4]{\frac{1}{32}}$
202152	Simplify	(11+x)/(4x)-3/2	$\frac{11 + x}{4 x} - \frac{3}{2}$
202153	Graph	y>2 x<-2	$y > 2$ $x < - 2$
202154	Simplify	-m^24r^312r^-4*5m	$- m^{2} \cdot 4 r^{3} \cdot 12 r^{- 4} \cdot 5 m$
202155	Simplify	(i-5)^2-2(i-5)+6	${(i - 5)}^{2} - 2 (i - 5) + 6$
202156	Simplify	(2y+8)/(16+4y)	$\frac{2 y + 8}{16 + 4 y}$
202157	Factor	x^2+2x+(-15)	$x^{2} + 2 x + (- 15)$
202158	Factor by Grouping	1-bx-x+b	$1 - b x - x + b$
202159	Convert to Radical Form	45^(-3/2)*45^2	$45^{- \frac{3}{2}} \cdot 45^{2}$
202160	Solve for Z	X=(YZ)/6	$X = \frac{Y Z}{6}$
202161	Simplify	1/( square root of 2b^3)	$\frac{1}{\sqrt{2 b^{3}}}$
202162	Solve the Rational Equation for x	4 square root of x=6	$4 \sqrt{x} = 6$
202163	Solve the Inequality for x	6x+5>=7x	$6 x + 5 \geq 7 x$
202164	Find the x and y Intercepts	f(x)=1/2*e^(-x)-1	$f (x) = \frac{1}{2} \cdot e^{- x} - 1$
202165	Solve for A	(sec(x)-1)/(sec(x)+1)=(A-cos(x))/(B+cos(x))	$\frac{\sec (x) - 1}{\sec (x) + 1} = \frac{A - \cos (x)}{B + \cos (x)}$
202166	Simplify the Radical Expression	( fourth root of 48a^10)/( fourth root of 3a^2)	$\frac{\sqrt[4]{48 a^{10}}}{\sqrt[4]{3 a^{2}}}$
202167	Simplify	(5+ square root of 7)	$(5 + \sqrt{7})$
202168	Find the Excluded Values	((x^2+10x+25)/(x-5))÷((x^2-25)/(5x+10))	$\frac{x^{2} + 10 x + 25}{x - 5} \div \frac{x^{2} - 25}{5 x + 10}$
202169	Simplify the Radical Expression	x square root of 50x-3 square root of 32x^3	$x \sqrt{50 x} - 3 \sqrt{32 x^{3}}$
202170	Simplify	3/x+10/(8x)	$\frac{3}{x} + \frac{10}{8 x}$
202171	Simplify	(4a^2b^0c^-5)^3	${(4 a^{2} b^{0} c^{- 5})}^{3}$
202172	Evaluate	(x^2y)^4	${(x^{2} y)}^{4}$
202173	Simplify	((a^3b^-4c^0)^-2)/((a^2b^5c^3)^-4)	$\frac{{(a^{3} b^{- 4} c^{0})}^{- 2}}{{(a^{2} b^{5} c^{3})}^{- 4}}$
202174	Simplify	(6x^2+5xy-6y^2)/(3x^2-5xy+2y^2)	$\frac{6 x^{2} + 5 x y - 6 y^{2}}{3 x^{2} - 5 x y + 2 y^{2}}$
202175	Simplify	7/3a-8/5a+4/15a	$\frac{7}{3} a - \frac{8}{5} a + \frac{4}{15} a$
202176	Solve for x	(6-x)/x=10	$\frac{6 - x}{x} = 10$
202177	Simplify	( fourth root of 32)/( cube root of 2)	$\frac{\sqrt[4]{32}}{\sqrt[3]{2}}$
202178	Solve for x	4x^5=128	$4 x^{5} = 128$
202179	Simplify	square root of 3x^4y* square root of 15x^3y^2	$\sqrt{3 x^{4} y} \cdot \sqrt{15 x^{3} y^{2}}$
202180	Simplify the Radical Expression	cube root of 4x^2* cube root of 8x^7	$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{8 x^{7}}$
202181	Solve for x	7x-(3x+5)-8=1/2(8x+20)-7x+5	$7 x - (3 x + 5) - 8 = \frac{1}{2} (8 x + 20) - 7 x + 5$
202182	Simplify	(3y)/(y-4)-(11y)/(4y-16)	$\frac{3 y}{y - 4} - \frac{11 y}{4 y - 16}$
202183	Solve for x	square root of x+6 = square root of 4x	$\sqrt{x + 6} = \sqrt{4 x}$
202184	Solve for y	y = square root of 36x-36	$y = \sqrt{36 x - 36}$
202185	Expand the Logarithmic Expression	log base b of bx	$\log_{b} (b x)$
202186	Find the Degree, Leading Term, and Leading Coefficient	h(x)=5/3x^2- square root of 7x^4+8x^3-1/2+x	$h (x) = \frac{5}{3} x^{2} - \sqrt{7} x^{4} + 8 x^{3} - \frac{1}{2} + x$
202187	Find the Excluded Values	(x^2-4)/(4x^2-8x)	$\frac{x^{2} - 4}{4 x^{2} - 8 x}$
202188	Solve for x	(x^3)/8-5=3	$\frac{x^{3}}{8} - 5 = 3$
202189	Simplify	4x^2(3x^3+6x-3)+3x^3(2x^2-5x+1)	$4 x^{2} (3 x^{3} + 6 x - 3) + 3 x^{3} (2 x^{2} - 5 x + 1)$
202190	Solve for q	-20+11q=10q	$- 20 + 11 q = 10 q$
202191	Simplify	( square root of 2)÷( cube root of 2)	$\sqrt{2} \div \sqrt[3]{2}$
202192	Simplify	(2(x+4))/(4(x+2))	$\frac{2 (x + 4)}{4 (x + 2)}$
202193	Solve for x	16xy^2-y^6=8	$16 x y^{2} - y^{6} = 8$
202194	Solve for v	3(1.4v-1)=0.2v+1	$3 (1.4 v - 1) = 0.2 v + 1$
202195	Solve for n	4x^2+nx=-9	$4 x^{2} + n x = - 9$
202196	Evaluate	-3^-1+3	$- 3^{- 1} + 3$
202197	Simplify	(3x+5)/(2x-1)+(7x+3)/(1-2x)	$\frac{3 x + 5}{2 x - 1} + \frac{7 x + 3}{1 - 2 x}$
202198	Simplify the Radical Expression	square root of 3^3*6^3	$\sqrt{3^{3}} \cdot 6^{3}$
202199	Solve for m₂	(1-2/3m_2)(1)=m_2+2/3	$(1 - \frac{2}{3} m_{2}) (1) = m_{2} + \frac{2}{3}$
202200	Write in Exponential Form	(n root of a)^n	${(\sqrt[n]{a})}^{n}$