Solve 8 x − 2 3 = 2 25 8x^{-\frac{2}{3}}=\frac{2}{25} 8 x − 3 2 = 2 5 2

− 1 1000 -\frac{1}{1000} − 1 0 0 0 1

1 1000 \frac{1}{1000} 1 0 0 0 1

Solve the simultaneous equations of 3 x × 9 2 x + 1 = 81 3^x\times9^{2x+1}=81 3 x × 9 2 x + 1 = 8 1 and 4 x × 8 − y = 0.5 4^x\times8^{-y}=0.5 4 x × 8 − y = 0 . 5 .

x = 2 11 , y = 5 11 x=\frac{2}{11},\ \ y=\frac{5}{11} x = 1 1 2 , y = 1 1 5

x = − 2 11 , y = 5 11 x=-\frac{2}{11},\ \ y=\frac{5}{11} x = − 1 1 2 , y = 1 1 5

x = 2 11 , y = − 5 11 x=\frac{2}{11},\ \ y=-\frac{5}{11} x = 1 1 2 , y = − 1 1 5

x = − 2 11 , y = − 5 11 x=-\frac{2}{11},\ \ y=-\frac{5}{11} x = − 1 1 2 , y = − 1 1 5

x = 5 11 , y = 2 11 x=\frac{5}{11},\ \ y=\frac{2}{11} x = 1 1 5 , y = 1 1 2

Solve the simultaneous equations of 7 5 y 4 9 x = 2401 \frac{7^{5y}}{49^x}=2401 4 9 x 7 5 y = 2 4 0 1 and 2 x ⋅ 4 ( 2 − y ) = 32 2^x\cdot4^{\left(2-y\right)}=\sqrt{32} 2 x ⋅ 4 ( 2 − y ) = 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> .

x = 1 2 , y = 1 x=\frac{1}{2},\ y=1 x = 2 1 , y = 1

x = − 1 2 , y = − 1 x=-\frac{1}{2},\ y=-1 x = − 2 1 , y = − 1

x = − 1 2 , y = 1 x=-\frac{1}{2},\ y=1 x = − 2 1 , y = 1

x = 1 2 , y = − 1 x=\frac{1}{2},\ y=-1 x = 2 1 , y = − 1

x = 1 , y = 1 2 x=1,\ y=\frac{1}{2} x = 1 , y = 2 1

Solve the simultaneous equations of 21 6 x 3 6 y = 1 129 6 ( x − 1 ) \frac{216^x}{36^y}=\frac{1}{\sqrt{1296^{\left(x-1\right)}}} 3 6 y 2 1 6 x = 1 2 9 6 ( x − 1 ) <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 and 3 ( 9 ( x ) ) = 24 3 ( y + 1 2 x ) 3\left(9^{\left(x\right)}\right)=243^{\left(y+\frac{1}{2}x\right)} 3 ( 9 ( x ) ) = 2 4 3 ( y + 2 1 x ) .

x = 6 13 , y = 2 13 x=\frac{6}{13},\ y=\frac{2}{13} x = 1 3 6 , y = 1 3 2

x = − 2 13 , y = 6 13 x=-\frac{2}{13},\ y=\frac{6}{13} x = − 1 3 2 , y = 1 3 6

x = 2 13 , y = − 6 13 x=\frac{2}{13},\ y=-\frac{6}{13} x = 1 3 2 , y = − 1 3 6

x = − 2 13 , y = − 6 13 x=-\frac{2}{13},\ y=-\frac{6}{13} x = − 1 3 2 , y = − 1 3 6

x = 2 13 , y = 6 13 x=\frac{2}{13},\ y=\frac{6}{13} x = 1 3 2 , y = 1 3 6

Laws of Indices (HOTS) solving index equations

Authored by Ting Ui

Mathematics

9th - 11th Grade

Used 354+ times

Laws of Indices (HOTS) solving index equations

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20 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $2^{\left(x+1\right)}\times4^{\left(2x-3\right)}=16^{\left(3x-2\right)}$

$\frac{7}{3}$

$\frac{3}{7}$

$-\frac{7}{3}$

$-\frac{3}{7}$

$\frac{4}{7}$

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Solve $\left(8^y\right)^y\cdot\frac{1}{32^y}=4$ (two answers)

$-\frac{1}{3}$

$\frac{1}{3}$

$-2$

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Solve $216^{\left(m^2-1\right)}=9^{4m}\cdot2^{8m}$ (two answers)

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{1}{6}$

$-3$

$-6$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\sqrt{32^{\left(x+2\right)}}=\frac{2}{8^x\times2^{\left(5-x\right)}}$

$-0.2$

$\frac{1}{2}$

$-2$

$-\frac{1}{2}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $9^{\left(2z-10\right)}=\frac{7^0}{\sqrt{27^{\left(z+3\right)}3^{\left(5z-1\right)}}}$

$\frac{1}{2}$

$-2$

$-\frac{1}{2}$

0.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $\left(-9\right)^{\left(1-2x\right)}=3^{-4}$

$\frac{2}{3}$

$-\frac{2}{3}$

$\frac{3}{2}$

$0.3$

$-\frac{3}{2}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $8x^{-\frac{2}{3}}=\frac{2}{25}$

$-\frac{1}{1000}$

$-1000$

0.0001

1000

$\frac{1}{1000}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $x^{\frac{1}{4}}=32x^{\frac{7}{8}}$

$-2$

$-\frac{1}{2}$

$\frac{1}{2}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$3^{\left(x+2\right)}=3\left(24+3^{\left(x-1\right)}\right)$

$\frac{1}{2}$

$-\frac{1}{2}$

$-2$

$\frac{3}{2}$

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve $6^n-2\left(6^{\left(n-2\right)}\right)=204$

$\frac{1}{3}$

$-\frac{1}{3}$

$-3$

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Laws of Indices (HOTS) solving index equations

Solve 2(x+1)×4(2x−3)=16(3x−2)2^{\left(x+1\right)}\times4^{\left(2x-3\right)}=16^{\left(3x-2\right)}2(x+1)×4(2x−3)=16(3x−2)

Solve (8y)y⋅132y=4\left(8^y\right)^y\cdot\frac{1}{32^y}=4(8y)y⋅32y1​=4 (two answers)

Solve 216(m2−1)=94m⋅28m216^{\left(m^2-1\right)}=9^{4m}\cdot2^{8m}216(m2−1)=94m⋅28m (two answers)

Solve 32(x+2)=28x×2(5−x)\sqrt{32^{\left(x+2\right)}}=\frac{2}{8^x\times2^{\left(5-x\right)}}32(x+2)​=8x×2(5−x)2​

Solve 9(2z−10)=7027(z+3)3(5z−1)9^{\left(2z-10\right)}=\frac{7^0}{\sqrt{27^{\left(z+3\right)}3^{\left(5z-1\right)}}}9(2z−10)=27(z+3)3(5z−1)​70​

Solve (−9)(1−2x)=3−4\left(-9\right)^{\left(1-2x\right)}=3^{-4}(−9)(1−2x)=3−4

Solve 8x−23=2258x^{-\frac{2}{3}}=\frac{2}{25}8x−32​=252​

Solve x14=32x78x^{\frac{1}{4}}=32x^{\frac{7}{8}}x41​=32x87​

3(x+2)=3(24+3(x−1))3^{\left(x+2\right)}=3\left(24+3^{\left(x-1\right)}\right)3(x+2)=3(24+3(x−1))

Solve 6n−2(6(n−2))=2046^n-2\left(6^{\left(n-2\right)}\right)=2046n−2(6(n−2))=204

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Discover more resources for Mathematics

Solve $2^{\left(x+1\right)}\times4^{\left(2x-3\right)}=16^{\left(3x-2\right)}$

Solve $\left(8^y\right)^y\cdot\frac{1}{32^y}=4$ (two answers)

Solve $216^{\left(m^2-1\right)}=9^{4m}\cdot2^{8m}$ (two answers)

Solve $\sqrt{32^{\left(x+2\right)}}=\frac{2}{8^x\times2^{\left(5-x\right)}}$

Solve $9^{\left(2z-10\right)}=\frac{7^0}{\sqrt{27^{\left(z+3\right)}3^{\left(5z-1\right)}}}$

Solve $\left(-9\right)^{\left(1-2x\right)}=3^{-4}$

Solve $8x^{-\frac{2}{3}}=\frac{2}{25}$

Solve $x^{\frac{1}{4}}=32x^{\frac{7}{8}}$

$3^{\left(x+2\right)}=3\left(24+3^{\left(x-1\right)}\right)$

Solve $6^n-2\left(6^{\left(n-2\right)}\right)=204$