Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
10301	Simplify	(x-4)(x-4)(x-6i)(x+6i)	$(x - 4) (x - 4) (x - 6 i) (x + 6 i)$
10302	Simplify	(x-(-1+i))(x-(-1-i))	$(x - (- 1 + i)) (x - (- 1 - i))$
10303	Simplify	(-(216t^9))^(1/3)	${(- (216 t^{9}))}^{\frac{1}{3}}$
10304	Simplify	((x-1)/2)^2	${(\frac{x - 1}{2})}^{2}$
10305	Simplify	(x-(3+4i))(x-(3-4i))	$(x - (3 + 4 i)) (x - (3 - 4 i))$
10306	Simplify	(x-(3-2i))(x-(3+2i))	$(x - (3 - 2 i)) (x - (3 + 2 i))$
10307	Simplify	((a^2)/b)^5((a^3b^2)/(c^3))^3	${(\frac{a^{2}}{b})}^{5} {(\frac{a^{3} b^{2}}{c^{3}})}^{3}$
10308	Simplify	((ab^2c^-3)/(2a^3b^-4))^-2	${(\frac{a b^{2} c^{- 3}}{2 a^{3} b^{- 4}})}^{- 2}$
10309	Simplify	((a^(1/12)b^-4)/(x^-1y))^4((x^-3b^-1)/(a^(4/3)y^(1/4)))	${(\frac{a^{\frac{1}{12}} b^{- 4}}{x^{- 1} y})}^{4} (\frac{x^{- 3} b^{- 1}}{a^{\frac{4}{3}} y^{\frac{1}{4}}})$
10310	Simplify	((e^x+e^(-x))/2)^2-((e^x-e^(-x))/2)^2	${(\frac{e^{x} + e^{- x}}{2})}^{2} - {(\frac{e^{x} - e^{- x}}{2})}^{2}$
10311	Simplify	((m^-2n^3)/(m^4n^-1))^2	${(\frac{m^{- 2} n^{3}}{m^{4} n^{- 1}})}^{2}$
10312	Simplify	((p^3)/(5q^3))^-4	${(\frac{p^{3}}{5 q^{3}})}^{- 4}$
10313	Simplify	((q^-1r^-1s^-5)/(r^-3sq^-7))^-1	${(\frac{q^{- 1} r^{- 1} s^{- 5}}{r^{- 3} s q^{- 7}})}^{- 1}$
10314	Simplify	((s^2t^-4)/(5s^-1t))^-2	${(\frac{s^{2} t^{- 4}}{5 s^{- 1} t})}^{- 2}$
10315	Simplify	(1/3*(x^4y^-3))^-2	${(\frac{1}{3} \cdot (x^{4} y^{- 3}))}^{- 2}$
10316	Simplify	((x^6)/(16y^-4))^(-1/2)	${(\frac{x^{6}}{16 y^{- 4}})}^{- \frac{1}{2}}$
10317	Simplify	((xy^-3z^-2)/(x^2y^4z^-3))^-3	${(\frac{x y^{- 3} z^{- 2}}{x^{2} y^{4} z^{- 3}})}^{- 3}$
10318	Simplify	(1/a)^2	${(\frac{1}{a})}^{2}$
10319	Simplify	((x^12y^-3)/(8y^(3/2)))^(-1/3)	${(\frac{x^{12} y^{- 3}}{8 y^{\frac{3}{2}}})}^{- \frac{1}{3}}$
10320	Simplify	((x^16y^-4)/(16y^(4/3)))^(-1/4)	${(\frac{x^{16} y^{- 4}}{16 y^{\frac{4}{3}}})}^{- \frac{1}{4}}$
10321	Simplify	((a^6y)/(y^4))^(5/2)	${(\frac{a^{6} y}{y^{4}})}^{\frac{5}{2}}$
10322	Simplify	(1/(x^2-5x-14))^(1/2)	${(\frac{1}{x^{2} - 5 x - 14})}^{\frac{1}{2}}$
10323	Solve for t	(9t+6)/(t(t+3))=7/(t+3)	$\frac{9 t + 6}{t (t + 3)} = \frac{7}{t + 3}$
10324	Solve for t	9^t=27	$9^{t} = 27$
10325	Solve for t	(At-b)/(c-b(1-2t))=3	$\frac{A t - b}{c - b (1 - 2 t)} = 3$
10326	Solve for t	log base 2 of square root of 2/64=t	$\log_{2} (\sqrt{\frac{2}{64}}) = t$
10327	Solve for t	t^2+4t+13=0	$t^{2} + 4 t + 13 = 0$
10328	Solve for t	log base 2 of t+1- log base 2 of t-1=3	$\log_{2} (t + 1) - \log_{2} (t - 1) = 3$
10329	Solve for t	t^4+2t^3-3t^2=0	$t^{4} + 2 t^{3} - 3 t^{2} = 0$
10330	Solve for t	3^(2t-5) = square root of 27	$3^{2 t - 5} = \sqrt{27}$
10331	Solve for t	1/81=27^(6t-5)	$\frac{1}{81} = 27^{6 t - 5}$
10332	Solve for t	1/8-t^2=0	$\frac{1}{8} - t^{2} = 0$
10333	Solve for t	9/(2-t)+3/(2+t)+6/(4-t^2)=0	$\frac{9}{2 - t} + \frac{3}{2 + t} + \frac{6}{4 - t^{2}} = 0$
10334	Solve for t	cot(t)^2=3	$\cot^{2} (t) = 3$
10335	Solve for t	e^(-t)=0.03	$e^{- t} = 0.03$
10336	Solve for t	0=32t-16t^2	$0 = 32 t - 16 t^{2}$
10337	Solve for t	104=101.6-3sin(pi/4t)	$104 = 101.6 - 3 \sin (\frac{π}{4} t)$
10338	Solve for t	104=101.8-7sin(pi/8t)	$104 = 101.8 - 7 \sin (\frac{π}{8} t)$
10339	Solve for t	-16t^2+160t=0	$- 16 t^{2} + 160 t = 0$
10340	Solve for t	s=1/13gt^2	$s = \frac{1}{13} g t^{2}$
10341	Solve for t	2=e^(0.09t)	$2 = e^{0.09 t}$
10342	Solve for t	s=1/7gt^2	$s = \frac{1}{7} g t^{2}$
10343	Solve for t	2p=p(1+0.08/12)^(12t)	$2 p = p {(1 + \frac{0.08}{12})}^{12 t}$
10344	Solve for t	3(1.04)^(3t)=8	$3 {(1.04)}^{3 t} = 8$
10345	Solve for t	300e^(0.06t)=1200	$300 e^{0.06 t} = 1200$
10346	Solve for t	4e^(6t)=6e^(5t)	$4 e^{6 t} = 6 e^{5 t}$
10347	Solve for t	3t-(2(t-1))/3=4	$3 t - \frac{2 (t - 1)}{3} = 4$
10348	Solve for t	20000(0.92)^t=16000(0.93)^t	$20000 {(0.92)}^{t} = 16000 {(0.93)}^{t}$
10349	Solve for t	32t-16t^2=0	$32 t - 16 t^{2} = 0$
10350	Solve for t	36t^2-12t+1=0	$36 t^{2} - 12 t + 1 = 0$
10351	Solve for t	600=-16t^2+803t	$600 = - 16 t^{2} + 803 t$
10352	Solve for x	4^(x+3)=128	$4^{x + 3} = 128$
10353	Solve for t	88=151t-16t^2	$88 = 151 t - 16 t^{2}$
10354	Solve for t	9900=900e^(0.15t)	$9900 = 900 e^{0.15 t}$
10355	Solve for t	cos(3t)=1/2	$\cos (3 t) = \frac{1}{2}$
10356	Solve for t	cos(t)=-( square root of 2)/2	$\cos (t) = - \frac{\sqrt{2}}{2}$
10357	Solve for t	cos(t)=-1/2	$\cos (t) = - \frac{1}{2}$
10358	Solve for t	cos(t)=-4/5	$\cos (t) = - \frac{4}{5}$
10359	Solve for t	cot(2t)=1	$\cot (2 t) = 1$
10360	Solve for t	csc(t)=2/( square root of 3)	$\csc (t) = \frac{2}{\sqrt{3}}$
10361	Solve for t	d=8cos((3pi)/4t)	$d = 8 \cos (\frac{3 π}{4} t)$
10362	Solve for R	R(1)=-500(1)^2+3000(1)	$R (1) = - 500 {(1)}^{2} + 3000 (1)$
10363	Solve for r	rcos(x)^2-rsin(x)^2=1	$r \cos^{2} (x) - r \sin^{2} (x) = 1$
10364	Solve for r	r=-4sin(x)	$r = - 4 \sin (x)$
10365	Solve for r	r=3cos(2x)	$r = 3 \cos (2 x)$
10366	Solve for R	p=(a^2R)/((r+R)^2)	$p = \frac{a^{2} R}{{(r + R)}^{2}}$
10367	Solve for r	r=0.65 log of 0.39e+1.45	$r = 0.65 \log (0.39 e) + 1.45$
10368	Solve for r	r=2sec(x)	$r = 2 \sec (x)$
10369	Solve for r	A=2pr(r+h)	$A = 2 p r (r + h)$
10370	Solve for p	g=(4pi^2pi)/(r^2)	$g = \frac{4 π^{2} π}{r^{2}}$
10371	Solve for r	96500=60000(1+r/12)^144	$96500 = 60000 {(1 + \frac{r}{12})}^{144}$
10372	Solve for r	V=1/3pir^2h	$V = \frac{1}{3} π r^{2} h$
10373	Solve for s	log of 5+r = log of 5s-2	$\log (5 + r) = \log (5 s - 2)$
10374	Solve for S	r = square root of (7S)/(pp)	$r = \sqrt{\frac{7 S}{p p}}$
10375	Solve for s	s=15/(1-1/700)	$s = \frac{15}{1 - \frac{1}{700}}$
10376	Solve for r	f=(mv^2)/r	$f = \frac{m v^{2}}{r}$
10377	Solve for r	theta=gr+gvt	$θ = g r + g v t$
10378	Solve for r	rsin(x)=6	$r \sin (x) = 6$
10379	Solve for r	rcos(x)=7	$r \cos (x) = 7$
10380	Solve for s	log base 3 of s+45- log base 3 of s+5 = log base 3 of s	$\log_{3} (s + 45) - \log_{3} (s + 5) = \log_{3} (s)$
10381	Solve for s	9-2s=2(9-st)	$9 - 2 s = 2 (9 - s t)$
10382	Solve for t	(1+0.10/12)^(12t)=2	${(1 + \frac{0.1}{12})}^{12 t} = 2$
10383	Solve for s	s=4m+4u	$s = 4 m + 4 u$
10384	Solve for s	s-6 = square root of 12s+36	$s - 6 = \sqrt{12 s + 36}$
10385	Solve for t	( square root of 3)/(9^-4)=t^(3/2)	$\frac{\sqrt{3}}{9^{- 4}} = t^{\frac{3}{2}}$
10386	Solve for t	1/2+1/7=1/t	$\frac{1}{2} + \frac{1}{7} = \frac{1}{t}$
10387	Solve for t	(6^(3/2))/(( square root of 2)^3)=t^(2/3)	$\frac{6^{\frac{3}{2}}}{{(\sqrt{2})}^{3}} = t^{\frac{2}{3}}$
10388	Solve for t	1/8*(4t-5)=11/8t-(t+5)/16	$\frac{1}{8} \cdot (4 t - 5) = \frac{11}{8} t - \frac{t + 5}{16}$
10389	Solve for v	4v^2-3=11v	$4 v^{2} - 3 = 11 v$
10390	Solve for v	F=(gMv^2)/r	$F = \frac{g M v^{2}}{r}$
10391	Solve for v	5v^2=-7v-2	$5 v^{2} = - 7 v - 2$
10392	Solve for v	v=3i-4j	$v = 3 i - 4 j$
10393	Find the Directrix	x^2=12y	$x^{2} = 12 y$
10394	Solve for v	v=5i+3j	$v = 5 i + 3 j$
10395	Solve for v	v=6i+3j	$v = 6 i + 3 j$
10396	Solve for v	v=6i+8j	$v = 6 i + 8 j$
10397	Solve for v	v=-7i+24j	$v = - 7 i + 24 j$
10398	Solve for v	x=(w(6-v))/z	$x = \frac{w (6 - v)}{z}$
10399	Solve for v	v^2=-36	$v^{2} = - 36$
10400	Solve for w	((w+2)(w-11))/(w-8)=0	$\frac{(w + 2) (w - 11)}{w - 8} = 0$