Indices (Exponents) - ICSE STD 9 MATHEMATICS Questions

Q 1[2 Mark Question Answer]2 Marks

Solve for $x : (13)^{\sqrt x} = 4^4 - 3^4 - 6$

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Q 2[2 Mark Question Answer]2 Marks

If $3^{x + 1}= 9^{x - 3},$ find the value of $2^{1 + x}.$

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Q 3[2 Mark Question Answer]2 Marks

Solve : $3^{x-1}\times 5^{2y-3}= 225.$

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Q 4[2 Mark Question Answer]2 Marks

Evaluate $: \left(\frac{x^q}{x^r}\right)^{\frac{1}{q r}} \times\left(\frac{x^r}{x^p}\right)^{\frac{1}{r p}} \times\left(\frac{x^p}{x^q}\right)^{\frac{1}{p q}}$

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Q 5[2 Mark Question Answer]2 Marks

Solve :$4^{x - 2}- 2^{x + 1}= 0$

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Q 6[3 marks sum]3 Marks

If $\frac{9^n \cdot 3^2 \cdot 3^n-(27)^n}{\left(3^m \cdot 2\right)^3}=3^{-3}$Show that$: \mathrm{m}-\mathrm{n}=1$.

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Q 7[3 marks sum]3 Marks

If $\left(\frac{a^{-1} b^2}{a^2 b^{-4}}\right)^7 \div\left(\frac{a^3 b^{-5}}{a^{-2} b^3}\right)^{-5}=a^x \cdot b^y$, find $x+y$

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Q 8[3 marks sum]3 Marks

Simplify$ : \frac{3 \times 9^{n+1}-9 \times 3^{2 n}}{3 \times 3^{2 n+3}-9^{n+1}}$

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Q 9[3 marks sum]3 Marks

Evaluate $: \frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$

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Q 10[3 marks sum]3 Marks

Prove that $: \frac{a+b+c}{a^{-1} b^{-1}+b^{-1} c^{-1}+c^{-1} a^{-1}}=a b c$

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Q 11[4 marks sum]4 Marks

If $3^{4 x}=(81)^{-1}$ and $10^{\frac{1}{y}}=0.0001$, Find the value of $2^{-x} \times 16^y$

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Q 12[4 marks sum]4 Marks

If $2^{\mathrm{x}}=4^{\mathrm{y}}=8^{\mathrm{z}}$ and $\frac{1}{2 x}+\frac{1}{4 y}+\frac{1}{8 z}=4$, find the value of $\mathrm{x}$.

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Q 13[4 marks sum]4 Marks

Prove that : $\frac{a^{-1}}{a^{-1}+b^{-1}}+\frac{a^{-1}}{a^{-1}-b^{-1}}=\frac{2}{b^2-a^2}$

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Q 14[4 marks sum]4 Marks

If $m=\sqrt[3]{15}$ and $n=\sqrt[3]{14}$, find the value of $m-n-\frac{1}{m^2+m n+n^2}$

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Q 15[4 marks sum]4 Marks

Evaluate : $(64)^{\frac{2}{3}}-\sqrt[3]{125}-\frac{1}{2^{-5}}+(27)^{-\frac{2}{3}} \times\left(\frac{25}{9}\right)^{-\frac{1}{2}} \mathrm{}$

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Q 16[5 marks sum]5 Marks

Solve $x$ and $y$ if $:(\sqrt{32 } )^x \div 2^{y+1}=1$ and $8^y-16^{4-x / 2}=0$

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Q 17[5 marks sum]5 Marks

Find the values of $m$ and $n$ if :$4^{2 m}=(\sqrt[3]{16})^{-\frac{6}{n}}=(\sqrt{8})^2$

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Q 18[5 marks sum]5 Marks

Solve : $8 \times 2^{2 x}+4 \times 2^{x+1}=1+2^x$

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Q 19[5 marks sum]5 Marks

Simplify :$\frac{3 \times 27^{n+1}+9 \times 3^{3 n-1}}{8 \times 3^{3 n}-5 \times 27^n}$

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Q 20[5 marks sum]5 Marks

If $2160=2^a \cdot 3^b \cdot 5^c$, find $a, b$ and $c$. Hence calculate the value of $3^a \times 2^{-b} \times 5^{-c}$.

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Indices (Exponents) question types

Indices (Exponents) questions

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Indices (Exponents) MATHEMATICS - Indices (Exponents)

Indices (Exponents) question types

Indices (Exponents) questions

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