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MATHS [1 Mark Question Answer]

Exponents (Including Laws of Exponents) · ICSE STD 7 (ICSE - English Medium). 25 questions.

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[1 Mark Question Answer]

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25 questions · timed · auto-graded

Question 11 Mark
Simplify and express the Solution in the positive exponent form:
$\left(a^3 b^{-5}\right)^{-2}=a^{3 \times-2} b^{-5 \times-2}$
Answer

$\begin{aligned} & \left(a^3 b^{-5}\right)^{-2}=a^{3 \times-2} b^{-5 \times-2} \\ & =a^{-6} b^{10}=\frac{b^{10}}{a^6}\end{aligned}$
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Question 21 Mark
Simplify, giving Solution with positive index
$(-2)^2 \times(0)^3 \times(3)^3$
Answer
$(-2)^2 \times(0)^3 \times(3)^3$
$=4 \times 0 \times 27=0$
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Question 31 Mark
Simplify, giving Solution with positive index
$\left(10^2\right)^3\left(x^8\right)^{12}$
Answer
$\left(10^2\right)^3\left(x^8\right)^{12}$
$=10^{2 \times 3} x^{8 \times 12}=10^6 x^{96}$
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Question 41 Mark
Simplify, giving Solution with positive index
$2^{4 \mathrm{a}} \cdot 2^{3 \mathrm{a}} \cdot 2^{-\mathrm{a}}$
Answer

$\begin{aligned} & 2^{4 \mathrm{a}+3 \mathrm{a}-\mathrm{a}} \\ & =2^{7 \mathrm{a}-\mathrm{a}}=2^{6 \mathrm{a}}\end{aligned}$
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Question 51 Mark
Simplify, giving Solution with positive index
$x^{2 a+7} \cdot x^{2 a-8}$
Answer
$x^{2 a+7} \cdot x^{2 a-8}$
$=\mathrm{x}^{2 a+7+2 a-8}=\mathrm{x}^{4 a-1}$
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Question 61 Mark
Simplify, giving Solution with positive index
$\left(5 a^2 b\right)\left(2 a b^2\right)\left(a^3 b\right)$
Answer
$\left(5 a^2 b\right)\left(2 a b^2\right)\left(a^3 b\right)$
$=5 \cdot 2 \cdot a^{2+1+3} b^{1+2+1}=10 a^6 b^4$
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Question 71 Mark
Simplify, giving Solution with positive index
$x^2 y^3 \cdot 6 x^5 y \cdot 9 x^3 y^4$
Answer
$x^2 y^3 \cdot 6 x^5 y \cdot 9 x^3 y^4$
$=6 \times 9 \times x^2+5+3 y^{3+1+4}=54 x^{10} y^8$
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Question 81 Mark
Simplify, giving Solution with positive index
$2 b^6 \cdot b^3 \cdot 5 b^4$
Answer
$2 b^6 \cdot b^3 \cdot 5 b^4$
$=2 \times 5 \times b^{6+3+4}=10 b^{13}$​​​​​​​
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Question 91 Mark
Evaluate: $5^4 \div 5^3 \times 5^5$
Answer

$\begin{aligned} & 5^4 \div 5^3 \times 5^5 \\ & =\frac{5^4}{5^3} \times 5^5=5^{4-3+5}=5^6\end{aligned}$
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Question 101 Mark
Evaluate: $5^4 \times 5^3+5^5$
Answer

$\begin{aligned} & 5^4 \times 5^3+5^5=\frac{5^4 \times 5^3}{5^5} \\ & =5^{4+3-5}=5^{7-5}=5^2\end{aligned}$
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Question 161 Mark
If $a=2$ and $b=3$, find the value of: $(a x b)^b$
 
Answer
$(a \times b)^b==(2 \times 3)^3=(6)^3=6 \times 6 \times 6=216$
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Question 171 Mark
If $a =2$ and $b =3$, find the value of: $( a \times b )^{ a }$
 
Answer
$(a \times b)^3=(2 \times 3)^2-(6)^2=6 \times 6=36$
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[1 Mark Question Answer] - MATHS STD 7 Questions - Vidyadip