Selina solutions for Concise Mathematics [English] Class 8 ICSE chapter 2 - Exponents [Latest edition]

Evaluate:

${\displaystyle (3^{-1}\times 9^{-1})÷3^{-2}}$

Evaluate:

${\displaystyle (3^{-1}\times 4^{-1})÷6^{-1}}$

Evaluate:

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

Evaluate:

${\displaystyle {(3^{-1}÷4^{-1})}^2}$

Evaluate:

${\displaystyle (2^2+3^2)\times {\left(\frac{1}{2}\right)}^2}$

Evaluate:

${\displaystyle (5^2-3^2)\times {\left(\frac{2}{3}\right)}^{-3}}$

Evaluate:

${\displaystyle [{\left(\frac{1}{4}\right)}^{-3}-{\left(\frac{1}{3}\right)}^{-3}]÷{\left(\frac{1}{6}\right)}^{-3}}$

Evaluate:

${\displaystyle {\left[{(-\frac{3}{4})}^{-2}\right]}^2}$

Evaluate:

${\displaystyle {\left\{{\left(\frac{3}{5}\right)}^{-2}\right\}}^{-2}}$

Evaluate:

${\displaystyle (5^{-1}\times 3^{-1})÷6^{-1}}$

If 1125 = 3^m x 5ⁿ, find m and n

Find x, if 9 x 3^x = (27) ^2x-3

Compute:

${\displaystyle 1^8\times 3^0\times 5^3\times 2^2}$

Compute:

${\displaystyle {\left(4^7\right)}^2\times {\left(4^{-3}\right)}^4}$

Compute:

${\displaystyle {(2^{-9}÷2^{-11})}^3}$

Compute:

${\displaystyle {\left(\frac{2}{3}\right)}^{-4}\times {\left(\frac{27}{8}\right)}^{-2}}$

Compute:

${\displaystyle {\left(\frac{56}{28}\right)}^0÷{\left(\frac{2}{5}\right)}^3\times \frac{16}{25}}$

Compute:

${\displaystyle {\left(12\right)}^{-2}\times 3^3}$

Compute:

${\displaystyle {(-5)}^4\times {(-5)}^6÷{(-5)}^9}$

Compute:

${\displaystyle {(-\frac{1}{3})}^4÷{(-\frac{1}{3})}^8\times {(-\frac{1}{3})}^5}$

Compute:

${\displaystyle 9^0\times 4^{-1}÷2^{-4}}$

Compute:

${\displaystyle {\left(625\right)}^{-\frac{3}{4}}}$

Compute:

${\displaystyle {\left(\frac{27}{64}\right)}^{-\frac{2}{3}}}$

Compute:

${\displaystyle {\left(\frac{1}{32}\right)}^{-\frac{2}{5}}}$

Compute:

${\displaystyle {\left(125\right)}^{-\frac{2}{3}}÷{\left(8\right)}^{\frac{2}{3}}}$

Compute:

${\displaystyle {\left(243\right)}^{\frac{2}{5}}÷{\left(32\right)}^{-\frac{2}{5}}}$

Compute:

${\displaystyle {(-3)}^4-{\left(\sqrt[4]{3}\right)}^0\times {(-2)}^5÷{\left(64\right)}^{\frac{2}{3}}}$

Compute:

${\displaystyle {\left(27\right)}^{\frac{2}{3}}÷{\left(\frac{81}{16}\right)}^{-\frac{1}{4}}}$

Simplify:

${\displaystyle 8^{\frac{4}{3}}+{25}^{\frac{3}{2}}-{\left(\frac{1}{27}\right)}^{-\frac{2}{3}}}$

Simplify:

${\displaystyle {\left[{\left(64\right)}^{-2}\right]}^{-3}÷{\left[{\left\{{(-8)}^2\right\}}^3\right]}^2}$

Simplify:

${\displaystyle (2^{-3}-2^{-4})(2^{-3}+2^{-4})}$

Evaluate:

${\displaystyle {(-5)}^0}$

Evaluate:

${\displaystyle 8^0+4^0+2^0}$

Evaluate:

${\displaystyle {(8+4+2)}^0}$

Evaluate:

${\displaystyle 4{\text{x}}^0}$

Evaluate:

${\displaystyle {\left(4\text{x}\right)}^0}$

Evaluate:

${\displaystyle {\left[{\left({10}^3\right)}^0\right]}^5}$

Evaluate:

${\displaystyle {\left(7{\text{x}}^0\right)}^2}$

Evaluate:

${\displaystyle 9^0+9^{-1}-9^{-2}+9^{\frac{1}{2}}-9^{-\frac{1}{2}}}$

Simplify:

${\displaystyle \frac{{\text{a}}^5{\text{b}}^2}{{\text{a}}^2{\text{b}}^{-3}}}$

Simplify:

${\displaystyle 15{\text{y}}^8÷3{\text{y}}^3}$

Simplify:

${\displaystyle {\text{x}}^{10}{\text{y}}^6÷{\text{x}}^3{\text{y}}^{-2}}$

Simplify:

${\displaystyle 5{\text{z}}^{16}÷15{\text{z}}^{-11}}$

Simplify:

${\displaystyle {\left(36{\text{x}}^2\right)}^{\frac{1}{2}}}$

Simplify:

${\displaystyle {\left(125{\text{x}}^{-3}\right)}^{\frac{1}{3}}}$

Simplify:

${\displaystyle {\left(2{\text{x}}^2{\text{y}}^{-3}\right)}^{-2}}$

Simplify:

${\displaystyle {\left(27{\text{x}}^{-3}{\text{y}}^6\right)}^{\frac{2}{3}}}$

Simplify:

${\displaystyle {(-2{\text{x}}^{\frac{2}{3}}{\text{y}}^{-\frac{3}{2}})}^6}$

Simplify:

${\displaystyle {\left({\text{x}}^{\text{a}+\text{b}}\right)}^{\text{a}-\text{b}}.{\left({\text{x}}^{\text{b}+\text{c}}\right)}^{\text{b}-\text{c}}.{\left({\text{x}}^{\text{c}+\text{a}}\right)}^{\text{c}-\text{a}}}$

Simplify:

${\displaystyle \sqrt[5]{{\text{x}}^{20}{\text{y}}^{-10}{\text{z}}^5}÷\frac{{\text{x}}^3}{{\text{y}}^3}}$

Simplify:

${\displaystyle {\left[\frac{256{\text{a}}^{16}}{81{\text{b}}^4}\right]}^{-\frac{3}{4}}}$

simplify and express as positive indice:

${\displaystyle {\left({\text{a}}^{-2}\text{b}\right)}^{-2}.{\left(\text{a}\text{b}\right)}^{-3}}$

Simplify and express as positive indice:

${\displaystyle {\left({\text{x}}^{\text{n}}{\text{y}}^{-\text{m}}\right)}^4\times {\left({\text{x}}^3{\text{y}}^{-2}\right)}^{-\text{n}}}$

Simplify and express as positive indice;

${\displaystyle {\left[\frac{125{\text{a}}^{-3}}{{\text{y}}^6}\right]}^{-\frac{1}{3}}}$

Simplify and express as positive indice:

${\displaystyle {\left[\frac{32{\text{x}}^{-5}}{243{\text{y}}^{-5}}\right]}^{-\frac{1}{5}}}$

Simplify and express as positive indice:

${\displaystyle {\left({\text{a}}^{-2}\text{b}\right)}^{\frac{1}{2}}\times {\left(\text{a}{\text{b}}^{-3}\right)}^{\frac{1}{3}}}$

Simplify and express as positive indice:

(xy)^(m-n).(yz)^(n-l).(zx)^(l-m)

Show that:

${\displaystyle {\left(\frac{{\text{x}}^{\text{a}}}{{\text{x}}^{-\text{b}}}\right)}^{\text{a}-\text{b}}.{\left(\frac{{\text{x}}^{\text{b}}}{{\text{x}}^{-\text{c}}}\right)}^{\text{b}-\text{c}}.{\left(\frac{{\text{x}}^{\text{c}}}{{\text{x}}^{-\text{a}}}\right)}^{\text{c}-\text{a}}=1}$

Evaluate:

${\displaystyle \frac{x^{5+n}{\left(x^2\right)}^{3n+1}}{x^{7n-2}}}$

Evaluate:

${\displaystyle \frac{{\text{a}}^{2\text{n}+1}\times {\text{a}}^{(2\text{n}+1)(2\text{n}-1)}}{{\text{a}}^{\text{n}(4\text{n}-1)}\times {\left({\text{a}}^2\right)}^{2\text{n}+3}}}$

Prove that:

${\displaystyle {(\text{m}+\text{n})}^{-1}({\text{m}}^{-1}+{\text{n}}^{-1})={\left(\text{m}\text{n}\right)}^{-1}}$

Prove that:

${\displaystyle {\left(\frac{x^a}{x^b}\right)}^{\frac{1}{ab}}{\left(\frac{x^b}{x^c}\right)}^{\frac{1}{bc}}{\left(\frac{x^c}{x^a}\right)}^{\frac{1}{ca}}=1}$

Prove that:

${\displaystyle \frac{1}{1+{\text{x}}^{\text{a}-\text{b}}}+\frac{1}{1+{\text{x}}^{\text{b}-\text{a}}}=1}$

Find the value of n, when:

${\displaystyle {12}^{-5}\times {12}^{2\text{n}+1}={12}^{13}÷{12}^7}$

Find the value of n, when:

${\displaystyle \frac{{\text{a}}^{2\text{n}-3}\times {\left({\text{a}}^2\right)}^{\text{n}+1}}{{\left({\text{a}}^4\right)}^{-3}}={\left({\text{a}}^3\right)}^3÷{\left({\text{a}}^6\right)}^{-3}}$

Simplify:

${\displaystyle \frac{{\text{a}}^{2\text{n}+3}.{\text{a}}^{(2\text{n}+1)(\text{n}+2)}}{{\left({\text{a}}^3\right)}^{2\text{n}+1}.{\text{a}}^{\text{n}(2\text{n}+1)}}}$

Simplify:

${\displaystyle \frac{{\text{x}}^{2\text{n}+7}.{\left({\text{x}}^2\right)}^{3\text{n}+2}}{{\text{x}}^{4(2\text{n}+3)}}}$