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MATHS [2 Mark Question Answer]

Exponents · ICSE STD 8 (ICSE - English Medium). 24 questions.

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[2 Mark Question Answer]

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24 questions · timed · auto-graded

Question 12 Marks
Simplify and express as positive indice : $(x y)^{m-n} \cdot(y z)^{n-I} \cdot(z x)^{I-m}$
Answer
$ (x y)^{m-n} \cdot(y z)^{n-I} \cdot(z x)^{I-m}$
$ =x^{m-n} \cdot y^{m-n} \cdot y^{n-I} \cdot z^{n-I} \cdot x^{I-m} \cdot z^{I-m}$
$ =x^{m-n+I-m} \cdot y^{m-n+n-1} \cdot z^{n-I+I-m}$
$ =x^{I-n} \cdot y^{m-I} \cdot z^{n-m}$
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Question 22 Marks
Simplify and express as positive indice $; \left[\frac{125 a ^{-3}}{ y ^6}\right]^{-\frac{1}{3}}$
Answer
$ {\left[\frac{125 a ^{-3}}{ y ^6}\right]^{-\frac{1}{3}}=\left[\frac{5^3 a ^{-3}}{ y ^6}\right]^{-\frac{1}{3}}}$
$ =\frac{5^{3 \times \frac{-1}{3}} \cdot a ^{-3 \times \frac{-1}{3}}}{ y ^{6 \times \frac{-1}{3}}}$
$ =\frac{5^{-1} \cdot a ^1}{ y ^{-2}}$
$ =\frac{a \cdot y^2}{5}$
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Question 32 Marks
Simplify and express as positive indice : $\left(x^n y^{-m}\right)^4 \times\left(x^3 y^{-2}\right)^{-n}$
Answer
$ \left(x^n y^{-m}\right)^4 \times\left(x^3 y^{-2}\right)^{-n}$
$ =x^{4 n} y^{-4 m} \times x^{-3 n} y^{2 n}$
$ =x^{4 n-3 n} \cdot y^{-4 m+2 n}$
$ =x^n y^{-4 m+2 n}$
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Question 42 Marks
Simplify : $\left(36 x^2\right)^{\frac{1}{2}}$
Answer
$ \left(36 x^2\right)^{\frac{1}{2}}=(36)^{\frac{1}{2}} \cdot x^{2 \times \frac{1}{2}}$
$ =(6 \times 6)^{\frac{1}{2}} \cdot x =\left(6^2\right)^{\frac{1}{2}} \cdot x$
$ =6 x $
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Question 52 Marks
Simplify : $5 z^{16} \div 15 z^{-11}$
Answer
$ 5 z^{16} \div 15 z^{-11}=\frac{5 z^{16}}{15 z^{-11}}$
$ =\frac{5}{15} z^{16+11}$
$ =\frac{1}{3} z^{27}$
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Question 62 Marks
Simplify : $x^{10} y^6 \div x^3 y^{-2}$
Answer
$ x^{10} y^6 \div x^3 y^{-2} =\frac{x^{10} y^6}{x^3 y^{-2}}$
$ =x^{10-3} \cdot y^{6+2}$
$ =x^7 y^8$
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Question 92 Marks
Compute : $(125)^{-\frac{2}{3}} \div(8)^{\frac{2}{3}} $
Answer
$ (125)^{-\frac{2}{3}} \div(8)^{\frac{2}{3}}=\left(5^3\right)^{-\frac{2}{3}} \div\left(2^3\right)^{\frac{2}{3}}$
$ =5^{-\frac{2}{3} \times 3} \div 2^{3 \times \frac{2}{3}}$
$ =5^{-2} \div 2^2=\frac{1}{5^2} \times \frac{1}{2^2}$
$ =\frac{1}{25} \times \frac{1}{4}=\frac{1}{100}$
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Question 102 Marks
Compute : $\left(\frac{1}{32}\right)^{-\frac{2}{5}}$
Answer
$\left(\frac{1}{32}\right)^{-\frac{2}{5}} =\left(\frac{1}{2 \times 2 \times 2 \times 2 \times 2}\right)^{\frac{2}{5}}$
$ =\left(\frac{1}{2^5}\right)^{-\frac{2}{5}}=\frac{1}{2^{5 \times-\frac{2}{5}}}$
$ =\frac{1}{2^{-2}}=2^2=4$
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Question 112 Marks
Compute : $9^0 \times 4^{-1} \div 2^{-4}$
Answer
$ 9^0 \times 4^{-1} \div 2^{-4}=1 \times \frac{1}{4^1} \times \frac{1}{2^{-4}}$
$ =1 \times \frac{1}{4} \times 2^4=1 \times \frac{1}{2^2} \times 2^4$
$ =2^{4-2}=2^2=4$
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Question 122 Marks
Compute : $\left(-\frac{1}{3}\right)^4 \div\left(-\frac{1}{3}\right)^8 \times\left(-\frac{1}{3}\right)^5$
Answer
$ \left(-\frac{1}{3}\right)^4 \div\left(-\frac{1}{3}\right)^8 \times\left(-\frac{1}{3}\right)^5$
$ =\left(-\frac{1}{3}\right)^4 \times \frac{1}{\left(-\frac{1}{3}\right)^8} \times\left(-\frac{1}{3}\right)^5$
$ =\left(-\frac{1}{3}\right)^{4+5-8}=\left(-\frac{1}{3}\right)^{9-8}$
$ =-\frac{1}{3}$
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Question 132 Marks
Compute : $(-5)^4 \times(-5)^6 \div(-5)^9$
Answer
$ (-5)^4 \times(-5)^6 \div(-5)^9$
$ =\frac{(-5)^4}{1} \times \frac{(-5)^6}{1} \times \frac{1}{(-5)^9}$
$ =\frac{(-5)^{10}}{(-5)^9}=(-5)^{10-9}=-5$
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Question 142 Marks
Compute : $\left(2^{-9} \div 2^{-11}\right)^3$
Answer
$ \left(2^{-9} \div 2^{-11}\right)^3=\left(\frac{2^{-9}}{2^{-11}}\right)^3$
$ =\left(2^{-9+11}\right)^3$
$ =\left(2^2\right)^3=2^6$
$ =2 \times 2 \times 2 \times 2 \times 2 \times 2$
$ =64$
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Question 152 Marks
Compute : $\left(4^7\right)^2 \times\left(4^{-3}\right)^4$
Answer
$ \left(4^7\right)^2 \times\left(4^{-3}\right)^4$
$ =4^{14} \times 4^{-12}$
$ =4^{14-12}=4^2$
$ =4 \times 4$
$ =16 C $
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Question 162 Marks
Compute : $1^8 \times 3^0 \times 5^3 \times 2^2$
Answer
$ 1^8 \times 3^0 \times 5^3 \times 2^2$
$ =1 \times 1 \times 5 \times 5 \times 5 \times 2 \times 2$
$ =125 \times 4$
$ =500$
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Question 172 Marks
Evaluat : $\left(5^{-1} \times 3^{-1}\right) \div 6^{-1}$
Answer
$ \left(5^{-1} \times 3^{-1}\right) \div 6^{-1}$
$ =\left(\frac{1}{5} \times \frac{1}{3}\right) \div \frac{1}{6}$
$ =\frac{1}{15} \div \frac{1}{6}$
$ =\frac{1}{15} \times \frac{6}{1}=\frac{2}{5}$
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Question 182 Marks
Evaluate : $\left[\left(-\frac{3}{4}\right)^{-2}\right]^2$
Answer
$ {\left[\left(-\frac{3}{4}\right)^{-2}\right]^2=\left(-\frac{3}{4}\right)^{-2 \times 2}=\left(-\frac{3}{4}\right)^{-4}}$
$ =\left(\frac{4}{3}\right)^4=\frac{4 \times 4 \times 4 \times 4}{3 \times 3 \times 3 \times 3}$
$ =\frac{256}{81}=3 \frac{13}{81}$
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Question 192 Marks
Evaluate : $\left(5^2-3^2\right) \times\left(\frac{2}{3}\right)^{-3} \text{CV}$
Answer
$ \left(5^2-3^2\right) \times\left(\frac{2}{3}\right)^{-3}$
$ =(5 \times 5)-(3 \times 3) \times\left(\frac{3}{2}\right)^3$
$ =25-9 \times\left(\frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}\right)$
$ =16 \times \frac{27}{8}=54$
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Question 202 Marks
Evaluate : $\left(2^2+3^2\right) \times\left(\frac{1}{2}\right)^2$
Answer
$ \left(2^2+3^2\right) \times\left(\frac{1}{2}\right)^2$
$ =(2 \times 2)+(3 \times 3) \times\left(\frac{1}{2} \times \frac{1}{2}\right)$
$ =4+9 \times \frac{1}{4}=\frac{13}{4}=3 \frac{1}{4}$
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Question 212 Marks
Evaluate : $\left(3^{-1} \div 4^{-1}\right)^2$
Answer
$ \left(3^{-1} \div 4^{-1}\right)^2$
$ =\left(\frac{1}{3} \div \frac{1}{4}\right)^2$
$ =\left(\frac{1}{3} \times \frac{4}{1}\right)^2=\left(\frac{4}{3}\right)^2$
$ =\frac{16}{9}=1 \frac{7}{9}$
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Question 222 Marks
Evaluate : $\left(2^{-1}+3^{-1}\right)^3$
Answer
$ \left(2^{-1}+3^{-1}\right)^3$
$ =\left(\frac{1}{2}+\frac{1}{3}\right)^3=\left(\frac{1 \times 3}{2 \times 3}+\frac{1 \times 2}{3 \times 2}\right)^3$
$ =\left(\frac{3+2}{6}\right)^3=\left(\frac{5}{6}\right)^3$
$ =\frac{5 \times 5 \times 5}{6 \times 6 \times 6}=\frac{125}{216}$
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Question 232 Marks
Evaluate : $\left(3^{-1} \times 4^{-1}\right) \div 6^{-1}$
Answer
$ \left(3^{-1} \times 4^{-1}\right) \div 6^{-1}$
$ =\left(\frac{1}{3} \times \frac{1}{4}\right) \div \frac{1}{6}$
$ =\frac{1}{12} \div \frac{1}{6}$
$ =\frac{1}{12} \times \frac{6}{1}=\frac{1}{2}$
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Question 242 Marks
Evaluate : $\left(3^{-1} \times 9^{-1}\right) \div 3^{-2}$
Answer
$ \left(3^{-1} \times 9^{-1}\right) \div 3^{-2}$
$ =\left(\frac{1}{3} \times \frac{1}{9}\right) \div \frac{1}{3} \times \frac{1}{3}$
$ =\frac{1}{27} \div \frac{1}{9}$
$ =\frac{1}{27} \times \frac{9}{1}=\frac{1}{3}$
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