Math Formula Sheet

Algebra → Exponents → Powers

MR-107

Simplify the following expression:

$243^{\frac{1}{5}} - {(\frac{1}{81})}^{\frac{1}{4}} + {(64 + 7, 5)}^{0} + {(9^{\frac{7}{8}} : 3^{\frac{5}{4}})}^{4}$

MR-117

Simplify the following expression:

$\frac{2^{- 2} \cdot 5^{3} \cdot 10^{- 3}}{2^{- 3} \cdot 5^{2} \cdot 10^{- 4}}$

MR-119

Simplify the following expression:

$\frac{2 a^{2}}{5 b^{- 5}} \div \frac{10 a^{- 3}}{6 b^{- 4}}$

MR-120

Calculate the value of the following expression:

${[6 - 4 {(\frac{7}{16})}^{0}]}^{- 2} + {(\frac{2}{3})}^{- 1} + \frac{1}{4}$

MR-121

Simplify the following expression:

$2 x^{- n} {(x^{n} - 1)}^{- 1} - 4 {(x^{2 n} - 1)}^{- 1} + 2 x^{- n} {(x^{n} + 1)}^{- 1}$

$x \neq 0$

MR-124

Simplify the following expression:

$\frac{2 x^{n} - 2 x^{- n}}{2 x^{n} + 2 x^{- n} + 4}$

$x \neq 0; x \neq - 1$

MR-851 / 1.a

Simplify the following expression:

$5^{0} + 3^{- 2} \cdot {(\frac{1}{9})}^{- 1}$

MR-852 / 1.b

Simplify the following expression:

${(a - b)}^{0} + 0, 1^{- 2} \cdot 10^{- 1} (a \neq b)$

MR-853 / 1.c

Simplify the following expression:

${(\frac{1}{2})}^{- 2} - {(\frac{1}{4})}^{- 1} \cdot 2^{- 2}$

MR-854 / 1.d

Simplify the following expression:

${({(1 \frac{1}{3})}^{- 1} - 2^{- 2})}^{- 3}$

MR-855 / 2.a

Simplify the following expression:

$0, 1^{- 4} + 0, 01^{- 3} + 0, 001^{- 2} + 0, 0001^{- 1} + 0, 00001^{- 0}$

MR-856 / 2.b

Simplify the following expression:

${(x + y)}^{0} + 0, 25^{- 1} + {(- 0, 5)}^{- 2} + {(0, 001^{0})}^{- 4} (x + y \neq 0)$

MR-857 / 3.a

Simplify the following expression:

$2^{- 4} \cdot {(\frac{1}{4})}^{- 2}$

MR-858 / 3.b

Simplify the following expression:

$2^{- 4} \cdot 0, 1^{- 4}$

MR-859 / 3.c

Simplify the following expression:

${(\frac{5}{2} - {(\frac{3}{5})}^{- 1})}^{- 1}$

MR-860 / 3.d

Simplify the following expression:

$\frac{2^{- 2} + 5 {(\frac{1}{2})}^{0}}{3 - {(\frac{2}{3})}^{- 2}}$

MR-861 / 3.e

Simplify the following expression:

$\frac{3^{- 2} - {(\frac{3}{4})}^{- 2}}{2 - {(\frac{1}{5})}^{- 1}}$

MR-862 / 3.f

Simplify the following expression:

${({(- \frac{2}{3})}^{- 3} + 3 \cdot 2^{- 3})}^{- 2}$

MR-863 / 4.a

Simplify the following expression:

$0, 5^{- 1} + 0, 25^{- 2} + 0, 125^{- 3} + 0, 0625^{- 4}$

MR-864 / 4.b

Simplify the following expression:

$1^{- 1} + 2^{- 2} + 3^{- 3} + {(- 1)}^{- 1} + {(- 2)}^{- 2} + {(- 3)}^{- 3}$

MR-865 / 4.c

Simplify the following expression:

$\frac{{(\frac{1}{10})}^{- 3} \cdot 10^{5}}{{(\frac{1}{1000})}^{3} \cdot 1000^{- 5}}$

MR-866 / 4.d

Simplify the following expression:

$\frac{0, 25^{- 2} \cdot 1, 75^{- 3}}{0, 75^{2} \cdot 1, 25^{3}}$

MR-867 / 4.e

Simplify the following expression:

$\frac{0, 1^{- 2} - {(0, 4)}^{0}}{2 \frac{2}{3} {(\frac{2}{3})}^{- 3} + {(- \frac{1}{3})}^{- 1}}$

MR-868 / 5.b

Simplify the following expression:

$A = \frac{1^{- 1} + 2^{- 2}}{{(\frac{2}{3})}^{- 2} + 4^{- 1} \cdot 5 + 0, 5^{- 2}}$

MR-869 / 5.a

Simplify the following expression:

$A = \frac{{({(- 12)}^{- 3})}^{- 2} \cdot 75^{- 1} \cdot {(- 4)}^{0}}{{(25^{- 1})}^{4} \cdot 6^{6} \cdot 10^{4}}$

MR-871 / 11.a

Hozza egyszerűbb alakra a következő kifejezést:

$\frac{27 x^{- 2} y^{- 3}}{3^{2} x^{- 4} y^{2}}$

MR-872 / 11.b

Simplify the following expression:

$\frac{a^{- 3} a b^{- 2}}{2^{- 4} a^{3} b^{- 3}}$

MR-873 / 11.c

Simplify the following expression:

$\frac{x^{- 5} + 2 x^{2} - x}{x^{- 3}}$

MR-874 / 11.d

Simplify the following expression:

${(\frac{y^{- 2}}{x^{- 2}})}^{- 3} \div {(\frac{x^{- 1}}{y^{2}})}^{- 3}$

MR-875 / 11.e

Simplify the following expression:

$(\frac{a^{- 3}}{b^{- 3}}) \div {(\frac{a^{- 2}}{b^{3}})}^{- 2}$

MR-876 / 12.a

Simplify the following expression:

$(50^{x} + 30^{x} + 18^{x}) \cdot (5^{x} - 3^{x})$

MR-877 / 12.b

Simplify the following expression:

$(25^{x} + 20^{x} + 16^{x}) \cdot (5^{x} - 4^{x})$

MR-878 / 12.c

Simplify the following expression:

$\frac{a + b^{- 1}}{a + c {(b c + 1)}^{- 1}} - \frac{b^{- 1}}{a b c + a + c}$

MR-879 / 12.d

Simplify the following expression:

$\frac{a b^{- 1} - a^{- 1} b}{a^{- 2} - 2 a^{- 1} b^{- 1} + b^{- 2}}$

MR-880 / 13.a

Simplify the following expression:

${(\frac{2^{x} + 2^{- x}}{2})}^{2} - {(\frac{2^{x} - 2^{- x}}{2})}^{2}$

MR-881 / 13.b

Simplify the following expression:

$\frac{x^{- 4} - 25 y^{- 2}}{x^{- 2} - 5 y^{- 1}} \cdot x^{2} y {(y + 5 x^{2})}^{- 1}$

MR-882 / 13.c

Simplify the following expression:

$\frac{a^{- 4} - 9 b^{- 2}}{a^{- 2} - 3 b^{- 1}} \cdot \frac{{(b + 3 a^{2})}^{- 1}}{a^{- 2} b^{- 1}}$

MR-883 / 13.d

Simplify the following expression:

$\frac{a^{- 2} + b^{- 2}}{a^{- 1} + b^{- 1}} \cdot {(\frac{a^{2} + b^{2}}{a b})}^{- 1}$

MR-886 / 14.a

Simplify the following expression:

$({(\frac{5 x^{- 5}}{2 y^{- 2}})}^{- 2} \cdot {(\frac{y^{- 1}}{5 x^{- 1}})}^{- 3}) \div 10 x^{2} y^{- 3}$

MR-887 / 14.b

Simplify the following expression:

$({(\frac{3 a^{2}}{4 b^{- 3}})}^{- 3} \div {(\frac{9 a^{- 2} b}{4})}^{- 2}) \cdot \frac{b^{7}}{12 a^{- 11}}$

MR-888 / 14.c

Simplify the following expression:

$({(\frac{3 x^{- 3}}{5 y^{- 2}})}^{- 3} \div {(\frac{9 x^{- 2}}{5 y^{- 3}})}^{- 2}) \cdot \frac{x^{- 6} y}{15}$

MR-889 / 14.d

Simplify the following expression:

$({(\frac{2 a^{- 2}}{3 a b^{- 3}})}^{- 4} \div {(\frac{4 a^{- 2}}{3 b^{- 3}})}^{- 3}) \cdot \frac{1}{12 a^{5} b^{- 2}}$

MR-125 / 125.

Simplify the following expression:

${(\frac{a^{- 1} + b^{- 1}}{b a^{- 1} + a b^{- 1}})}^{- 1} + {(\frac{a^{- 1} + b^{- 1}}{2})}^{- 1} - \frac{a^{- 1} - b^{- 1}}{a^{- 1} \cdot b^{- 1}}$

MR-134 / 134.

Simplify the following expression:

${(\frac{2^{x} + 2^{- x}}{2})}^{2} - {(\frac{2^{x} - 2^{- x}}{2})}^{2} + 1$

MR-885 / 431.c

Solve the following equation:

$(1 + \sqrt{2}) x^{2} - 2 (1 - \sqrt{2}) x - 3 \sqrt{2} + 1 = 0$

MR-375 / 825.a

Find the cube of the given expressions:

$x + 2$

MR-180 / 825.b

Find the cube of the given expressions:

$x - 1$

MR-209 / 825.c

Find the cube of the given expressions:

$2 x - 3 y$