Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
202101	Find the Domain and Range	f(x)=(6x)^(1/2)+3	$f (x) = {(6 x)}^{\frac{1}{2}} + 3$
202102	Evaluate	1/(2^3-5)	$\frac{1}{2^{3} - 5}$
202103	Simplify	(x^3-y^3)/(x+y)*(x^2-y^2)/(x^2+xy+y^2)	$\frac{x^{3} - y^{3}}{x + y} \cdot \frac{x^{2} - y^{2}}{x^{2} + x y + y^{2}}$
202104	Graph	F(x)=e^(x+2)	$F (x) = e^{x + 2}$
202105	Solve for x	(5(x-8))/6=-7	$\frac{5 (x - 8)}{6} = - 7$
202106	Convert to a Decimal	14rad	$14$ radians
202107	Simplify the Radical Expression	fourth root of (3a^2)/(8b^3)	$\sqrt[4]{\frac{3 a^{2}}{8 b^{3}}}$
202108	Solve for x	10x+2x-100-100=2x+8x+300+200	$10 x + 2 x - 100 - 100 = 2 x + 8 x + 300 + 200$
202109	Write as a Single Logarithm	log base 3 of a^7+( log base 3 of a^4-2* log base 3 of b)	$\log_{3} (a^{7}) + (\log_{3} (a^{4}) - 2 \cdot \log_{3} (b))$
202110	Solve for d	1/4(d-3)=-15	$\frac{1}{4} (d - 3) = - 15$
202111	Find the Exact Value	2sin(pi/3)-3tan(pi/6)	$2 \sin (\frac{π}{3}) - 3 \tan (\frac{π}{6})$
202112	Simplify the Radical Expression	(-64)^(-1/3)	${(- 64)}^{- \frac{1}{3}}$
202113	Simplify	( square root of 2x)/(3- square root of 2x)	$\frac{\sqrt{2 x}}{3 - \sqrt{2 x}}$
202114	Find the Domain and Range	f(x)=1/4 cube root of x+2-5	$f (x) = \frac{1}{4} \sqrt[3]{x + 2} - 5$
202115	Find the Domain and Range	y=2(3)^(x-1)+4	$y = 2 {(3)}^{x - 1} + 4$
202116	Simplify	(2x)/(3x-18)+(x+1)/(x-6)	$\frac{2 x}{3 x - 18} + \frac{x + 1}{x - 6}$
202117	Simplify	square root of cube root of 64	$\sqrt[2]{\sqrt[3]{64}}$
202118	Simplify	x^-3y^-2z	$x^{- 3} y^{- 2} z$
202119	Simplify	2n+5.5-0.9n-8+4.5p	$2 n + 5.5 - 0.9 n - 8 + 4.5 p$
202120	Write in Standard Form	(4+2n^3)+(5n^3+2)	$(4 + 2 n^{3}) + (5 n^{3} + 2)$
202121	Solve for x	5x-(x+3)=1/3(9x+18)-5	$5 x - (x + 3) = \frac{1}{3} (9 x + 18) - 5$
202122	Simplify	fourth root of 6*3 fourth root of 6	$\sqrt[4]{6} \cdot 3 \sqrt[4]{6}$
202123	Simplify	(5 fourth root of 2)/(4 fourth root of 162)	$\frac{5 \sqrt[4]{2}}{4 \sqrt[4]{162}}$
202124	Simplify the Radical Expression	ninth root of 27	$\sqrt[9]{27}$
202125	Solve for m	m/3=(m^2)/6	$\frac{m}{3} = \frac{m^{2}}{6}$
202126	Simplify	28 root of 1/(p^6*p)	$\sqrt[28]{\frac{1}{p^{6} \cdot p}}$
202127	Simplify	(x^2y^2)/(y^2)	$\frac{x^{2} y^{2}}{y^{2}}$
202128	Subtract	9/12-3/6	$\frac{9}{12} - \frac{3}{6}$
202129	Simplify	(tan(theta)+cos(theta)csc(theta))/(sec(theta)csc(theta))	$\frac{\tan (θ) + \cos (θ) \csc (θ)}{\sec (θ) \csc (θ)}$
202130	Simplify the Radical Expression	4/( fourth root of 8m^2)	$\frac{4}{\sqrt[4]{8 m^{2}}}$
202131	Simplify	(x^(-1/3))^(-1/6)	${(x^{- \frac{1}{3}})}^{- \frac{1}{6}}$
202132	Simplify	((x+1) square root of x-2)/( square root of x^2-x-2)	$\frac{(x + 1) \sqrt{x - 2}}{\sqrt{x^{2} - x - 2}}$
202133	Simplify	(3 cube root of 32m^2)/( cube root of 4m)	$\frac{3 \sqrt[3]{32 m^{2}}}{\sqrt[3]{4 m}}$
202134	Find f(g(x))	f(x)=x^3+12x^2+25x-70 g(x)=x+7	$f (x) = x^{3} + 12 x^{2} + 25 x - 70$ $g (x) = x + 7$
202135	Graph	y>=3 y<=x y<=-1/2x+8	$y \geq 3$ $y \leq x$ $y \leq - \frac{1}{2} x + 8$
202136	Simplify the Radical Expression	fourth root of 1/32	$\sqrt[4]{\frac{1}{32}}$
202137	Simplify	(11+x)/(4x)-3/2	$\frac{11 + x}{4 x} - \frac{3}{2}$
202138	Graph	y>2 x<-2	$y > 2$ $x < - 2$
202139	Simplify	-m^24r^312r^-4*5m	$- m^{2} \cdot 4 r^{3} \cdot 12 r^{- 4} \cdot 5 m$
202140	Simplify	(i-5)^2-2(i-5)+6	${(i - 5)}^{2} - 2 (i - 5) + 6$
202141	Simplify	(2y+8)/(16+4y)	$\frac{2 y + 8}{16 + 4 y}$
202142	Factor	x^2+2x+(-15)	$x^{2} + 2 x + (- 15)$
202143	Factor by Grouping	1-bx-x+b	$1 - b x - x + b$
202144	Convert to Radical Form	45^(-3/2)*45^2	$45^{- \frac{3}{2}} \cdot 45^{2}$
202145	Solve for Z	X=(YZ)/6	$X = \frac{Y Z}{6}$
202146	Simplify	1/( square root of 2b^3)	$\frac{1}{\sqrt{2 b^{3}}}$
202147	Solve the Rational Equation for x	4 square root of x=6	$4 \sqrt{x} = 6$
202148	Solve the Inequality for x	6x+5>=7x	$6 x + 5 \geq 7 x$
202149	Find the x and y Intercepts	f(x)=1/2*e^(-x)-1	$f (x) = \frac{1}{2} \cdot e^{- x} - 1$
202150	Solve for A	(sec(x)-1)/(sec(x)+1)=(A-cos(x))/(B+cos(x))	$\frac{\sec (x) - 1}{\sec (x) + 1} = \frac{A - \cos (x)}{B + \cos (x)}$
202151	Simplify the Radical Expression	( fourth root of 48a^10)/( fourth root of 3a^2)	$\frac{\sqrt[4]{48 a^{10}}}{\sqrt[4]{3 a^{2}}}$
202152	Simplify	(5+ square root of 7)	$(5 + \sqrt{7})$
202153	Find the Excluded Values	((x^2+10x+25)/(x-5))÷((x^2-25)/(5x+10))	$\frac{x^{2} + 10 x + 25}{x - 5} \div \frac{x^{2} - 25}{5 x + 10}$
202154	Simplify the Radical Expression	x square root of 50x-3 square root of 32x^3	$x \sqrt{50 x} - 3 \sqrt{32 x^{3}}$
202155	Simplify	3/x+10/(8x)	$\frac{3}{x} + \frac{10}{8 x}$
202156	Simplify	(4a^2b^0c^-5)^3	${(4 a^{2} b^{0} c^{- 5})}^{3}$
202157	Evaluate	(x^2y)^4	${(x^{2} y)}^{4}$
202158	Simplify	((a^3b^-4c^0)^-2)/((a^2b^5c^3)^-4)	$\frac{{(a^{3} b^{- 4} c^{0})}^{- 2}}{{(a^{2} b^{5} c^{3})}^{- 4}}$
202159	Simplify	(6x^2+5xy-6y^2)/(3x^2-5xy+2y^2)	$\frac{6 x^{2} + 5 x y - 6 y^{2}}{3 x^{2} - 5 x y + 2 y^{2}}$
202160	Simplify	7/3a-8/5a+4/15a	$\frac{7}{3} a - \frac{8}{5} a + \frac{4}{15} a$
202161	Solve for x	(6-x)/x=10	$\frac{6 - x}{x} = 10$
202162	Simplify	( fourth root of 32)/( cube root of 2)	$\frac{\sqrt[4]{32}}{\sqrt[3]{2}}$
202163	Solve for x	4x^5=128	$4 x^{5} = 128$
202164	Simplify	square root of 3x^4y* square root of 15x^3y^2	$\sqrt{3 x^{4} y} \cdot \sqrt{15 x^{3} y^{2}}$
202165	Simplify the Radical Expression	cube root of 4x^2* cube root of 8x^7	$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{8 x^{7}}$
202166	Solve for x	7x-(3x+5)-8=1/2(8x+20)-7x+5	$7 x - (3 x + 5) - 8 = \frac{1}{2} (8 x + 20) - 7 x + 5$
202167	Simplify	(3y)/(y-4)-(11y)/(4y-16)	$\frac{3 y}{y - 4} - \frac{11 y}{4 y - 16}$
202168	Solve for x	square root of x+6 = square root of 4x	$\sqrt{x + 6} = \sqrt{4 x}$
202169	Solve for y	y = square root of 36x-36	$y = \sqrt{36 x - 36}$
202170	Expand the Logarithmic Expression	log base b of bx	$\log_{b} (b x)$
202171	Find the Degree, Leading Term, and Leading Coefficient	h(x)=5/3x^2- square root of 7x^4+8x^3-1/2+x	$h (x) = \frac{5}{3} x^{2} - \sqrt{7} x^{4} + 8 x^{3} - \frac{1}{2} + x$
202172	Find the Excluded Values	(x^2-4)/(4x^2-8x)	$\frac{x^{2} - 4}{4 x^{2} - 8 x}$
202173	Solve for x	(x^3)/8-5=3	$\frac{x^{3}}{8} - 5 = 3$
202174	Simplify	4x^2(3x^3+6x-3)+3x^3(2x^2-5x+1)	$4 x^{2} (3 x^{3} + 6 x - 3) + 3 x^{3} (2 x^{2} - 5 x + 1)$
202175	Solve for q	-20+11q=10q	$- 20 + 11 q = 10 q$
202176	Simplify	( square root of 2)÷( cube root of 2)	$\sqrt{2} \div \sqrt[3]{2}$
202177	Simplify	(2(x+4))/(4(x+2))	$\frac{2 (x + 4)}{4 (x + 2)}$
202178	Solve for x	16xy^2-y^6=8	$16 x y^{2} - y^{6} = 8$
202179	Solve for v	3(1.4v-1)=0.2v+1	$3 (1.4 v - 1) = 0.2 v + 1$
202180	Solve for n	4x^2+nx=-9	$4 x^{2} + n x = - 9$
202181	Evaluate	-3^-1+3	$- 3^{- 1} + 3$
202182	Simplify	(3x+5)/(2x-1)+(7x+3)/(1-2x)	$\frac{3 x + 5}{2 x - 1} + \frac{7 x + 3}{1 - 2 x}$
202183	Simplify the Radical Expression	square root of 3^3*6^3	$\sqrt{3^{3}} \cdot 6^{3}$
202184	Solve for m₂	(1-2/3m_2)(1)=m_2+2/3	$(1 - \frac{2}{3} m_{2}) (1) = m_{2} + \frac{2}{3}$
202185	Write in Exponential Form	(n root of a)^n	${(\sqrt[n]{a})}^{n}$
202186	Simplify	( square root of 8m^2)/( square root of 6m)	$\frac{\sqrt{8 m^{2}}}{\sqrt{6 m}}$
202187	Solve for y	-325/y=13	$- \frac{325}{y} = 13$
202188	Simplify	5 cube root of 9a^2*4 cube root of 3a	$5 \sqrt[3]{9 a^{2}} \cdot 4 \sqrt[3]{3 a}$
202189	Simplify	(4x)/(x+1)*(3x+3)/2	$\frac{4 x}{x + 1} \cdot \frac{3 x + 3}{2}$
202190	Simplify	(2^-1+5^-1)^2	${(2^{- 1} + 5^{- 1})}^{2}$
202191	Solve for n	fourth root of n+1=2	$\sqrt[4]{n + 1} = 2$
202192	Find the Exact Value	cos(-420 degrees )	$\cos (- 420 °)$
202193	Find the Degree, Leading Term, and Leading Coefficient	f(x)=2x+x^3+4	$f (x) = 2 x + x^{3} + 4$
202194	Solve the System of Equations	4x-1/3y=8 2/3x+1/3y=11/3	$4 x - \frac{1}{3} y = 8$ $\frac{2}{3} x + \frac{1}{3} y = \frac{11}{3}$
202195	Simplify the Radical Expression	1/( cube root of 5)	$\frac{1}{\sqrt[3]{5}}$
202196	Simplify	(7/9)÷(y/(y-11))	$\frac{7}{9} \div \frac{y}{y - 11}$
202197	Find g(f(x))	f(x)=3x+5 , g(x)=-2x-3	$f (x) = 3 x + 5$ , $g (x) = - 2 x - 3$
202198	Solve for x	3/4(1/6x+16)=3/7(4 3/8x-21)	$\frac{3}{4} (\frac{1}{6} x + 16) = \frac{3}{7} (4 \frac{3}{8} x - 21)$
202199	Evaluate	log base b of (x)^n	$\log_{b} ({(x)}^{n})$
202200	Subtract	(9a^3+6a^2-a)-(a^3+6a-3)	$(9 a^{3} + 6 a^{2} - a) - (a^{3} + 6 a - 3)$