Find the value of-i 30 - 4-1- 22ii 2-1- 4-1- 2-2iii 12-2 - 13 -2 - 14 -2iv 3-1-4-1-5-10v -23-2 2

(i) #160; (3^0 + 4^ 1)× 2^2 = (1+14 )× 2^2 =54×4= 5 #160; (ii) #160; (2^ 1× 4^ 1)÷ 2^ 2 =2^ 1×(2^2)^ 12^ 2 = 2^ 1+( 2)2^ 2 #160; #160; ...

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Byju's Answer

Standard VIII

Mathematics

Simplification of an Expression

Find the valu...

Question

Find the value of:
(i) $(3^{0} + 4^{- 1}) \times 2^{2}$

(ii) $(2^{- 1} \times 4^{- 1}) \div 2^{- 2}$
(iii) ${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}$
(iv) ${(3^{- 1} + 4^{- 1} + 5^{- 1})}^{0}$
(v) ${({(\frac{- 2}{3})}^{- 2})}^{2}$

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Solution

(i) $(3^{0} + 4^{- 1}) \times 2^{2} = (1 + \frac{1}{4}) \times 2^{2} = \frac{5}{4} \times 4 = 5$

(ii) $(2^{- 1} \times 4^{- 1}) \div 2^{- 2} = \frac{2^{- 1} \times {(2^{2})}^{- 1}}{2^{- 2}} = \frac{2^{- 1 + (- 2)}}{2^{- 2}}$

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

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

$= 2^{2} + 3^{2} + 4^{2} = 4 + 9 + 16 = 29$

(iv) $(3^{- 1} + 4^{- 1} + 5^{- 1})^{0} = 1$

(v) ${({(\frac{- 2}{3})}^{- 2})}^{2} = {(\frac{9}{4})}^{2} = \frac{81}{16}$

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Similar questions

Find the value of.

(i) (3⁰ + 4⁻¹) × 2² (ii) (2⁻¹ × 4⁻¹) ÷2⁻²

(iii) (iv) (3⁻¹ + 4⁻¹ + 5⁻¹)⁰

(v)

Find the value of:

(i) $(- 4) \div \frac{2}{3}$

(ii) $\frac{- 3}{5} \div 2$

(iii) $\frac{- 4}{5} \div - 3$

(iv) $\frac{- 1}{8} \div \frac{3}{4}$

(v) $\frac{- 2}{13} \div \frac{1}{7}$

(vi) $\frac{- 7}{12} \div \frac{- 2}{13}$

(vii) $\frac{3}{13} \div \frac{- 4}{65}$

Match the following:

$\begin{matrix} C o m p o u n d s & C o o r d i n a t i o n (A : B) (1) Z n S & (i) 8 : 8 (2) C s C l & (i i) 6 : 6 (3) N a C l & (i i i) 4 : 4 (4) N a_{2} O & (i v) 8 : 4 (5) C a F_{2} & (v) 4 : 8 \end{matrix}$

Q. Name the property under multiplication used in each of the following:
(i)

\frac{2}{3} \times \frac{4}{5} = \frac{4}{5} \times \frac{2}{3}

(ii)

(\frac{- 3}{4}) \times 1 = \frac{- 3}{4} = 1 \times (\frac{- 3}{4})

(iii)

(\frac{- 17}{28}) \times (\frac{- 28}{17}) = 1

(iv)

\frac{1}{5} \times (\frac{7}{8} \times \frac{4}{3}) = (\frac{1}{5} \times \frac{7}{8}) \times \frac{4}{3}

(v)

\frac{2}{7} \times (\frac{9}{10} + \frac{2}{5}) = \frac{2}{7} \times \frac{9}{10} + \frac{2}{7} \times \frac{2}{5}

Q. Observe the following patterns

1 = \frac{1}{2} (1 \times (1 + 1))

1 + 2 = \frac{1}{2} (2 \times (2 + 1))

1 + 2 + 3 = \frac{1}{2} (3 \times (3 + 1))

1 + 2 + 3 + 4 = \frac{1}{2} (4 \times (4 + 1))

and find the value of each of the following

1 + 2 + 3 + 4 + 5 + . . . . + 50

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Find the value of:(i) (30+4−1)×22(ii) (2−1×4−1)÷2−2(iii) (12)−2+(13)−2+(14)−2(iv) (3−1+4−1+5−1)0(v) ((−23)−2)2

(i) (30+4−1)×22=(1+14)×22=54×4=5(ii) (2−1×4−1)÷2−2=2−1×(22)−12−2=2−1+(−2)2−2 =2−32−2=2−3−(−2)=2−1=12(iii) (12)−2+(13)−2+(14)−2 =22+32+42=4+9+16=29(iv) (3−1+4−1+5−1)0=1(v) ((−23)−2)2=(94)2=8116

Find the value of:
(i) $(3^{0} + 4^{- 1}) \times 2^{2}$

(ii) $(2^{- 1} \times 4^{- 1}) \div 2^{- 2}$
(iii) ${(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}$
(iv) ${(3^{- 1} + 4^{- 1} + 5^{- 1})}^{0}$
(v) ${({(\frac{- 2}{3})}^{- 2})}^{2}$