Simplify-i 4-1 - 3-12ii 5-1 - 6-13iii 2-1-3-1-1iv 3-1 - 4-1-1 - 5-1

(i) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; — gt; (a−1 = 1/a) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp ...

Byju's Answer

Standard VIII

Mathematics

Inter Conversion between Standard and Normal Forms

Simplify:i 4-...

Question

Simplify:
(i) ${(4^{- 1} \times 3^{- 1})}^{2}$
(ii) ${(5^{- 1} \div 6^{- 1})}^{3}$
(iii) ${(2^{- 1} + 3^{- 1})}^{- 1}$
(iv) ${(3^{- 1} \times 4^{- 1})}^{- 1} \times 5^{- 1}$

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Solution

(i)
$left (4^{-1}times 3^{-1} right )^2=left (frac{1}{4}times frac{1}{3} right )^2$ ---> (a⁻¹ = 1/a)
$=left (frac{1}{12} right )^2$
$=frac{1^2}{12^2}$ ---> ((a/b)ⁿ = (aⁿ)/(bⁿ) )
$= \frac{1}{24}$

(ii)
$left (5^{-1}div 6^{-1} right )^3=left (frac{1}{5}div frac{1}{6} right )^3$ ---> (a⁻¹ = 1/a)
$=left (frac{1}{5}times6 right )^3$
= ${(\frac{6}{5})}^{3}$
= $\frac{{(6)}^{3}}{{(5)}^{3}}$ ---> ((a/b)ⁿ = (aⁿ)/(bⁿ) )

= $\frac{216}{125}$

(iii)
$(2^{- 1} + 3^{- 1})^{- 1} = {(\frac{1}{2} + \frac{1}{3})}^{- 1}$ ---> (a⁻¹ = 1/a)
= ${(\frac{5}{6})}^{- 1}$
$= \frac{1}{5 / 6}$ ---> (a⁻¹ = 1/a)
$= \frac{6}{5}$

(iv)
$left (3^{-1}times 4^{-1} right )^{-1}times 5^{-1}=left (frac{1}{3}times frac{1}{4} right )^{-1}times frac{1}{5}$ ---> (a⁻¹ = 1/a)
$=left (frac{1}{12}right )^{-1}times frac{1}{5}$
$= \frac{12}{5}$ ---> (a⁻¹ = 1/a)

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Similar questions

Q. Simplify:
(i)

{\{4^{- 1} \times 3^{- 1}\}}^{2}

(ii)

{\{5^{- 1} \div 6^{- 1}\}}^{3}

(iii)

{(2^{- 1} + 3^{- 1})}^{- 1}

(iv)

{\{3^{- 1} \times 4^{- 1}\}}^{- 1} \times 5^{- 1}

(v)

(4^{- 1} - 5^{- 1}) \div 3^{- 1}

Simplify:

$(i) {{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}} \div {(\frac{1}{4})}^{- 3} (i i) (3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3} (i i i) {(\frac{1}{2}) \times (- 4)^{- 1}}^{- 1} (i v) {[{{(\frac{- 1}{4})}^{2}}^{- 2}]}^{- 1} (v) {{(\frac{2}{3})}^{2}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1}$

Q. Simplify:
(i)

\{{(\frac{1}{3})}^{- 3} - {(\frac{1}{2})}^{- 3}\} \div {(\frac{1}{4})}^{- 3}

(ii)

(3^{2} - 2^{2}) \times {(\frac{2}{3})}^{- 3}

(iii)

{\{{(\frac{1}{2})}^{- 1} \times (- 4)^{- 1}\}}^{- 1}

(iv)

{[{\{{(\frac{- 1}{4})}^{2}\}}^{- 2}]}^{- 1}

(v)

{\{{(\frac{2}{3})}^{2}\}}^{3} \times {(\frac{1}{3})}^{- 4} \times 3^{- 1} \times 6^{- 1}

Find each of the following products:
$(i) (- 4) \times (- 5) \times (- 8) \times (- 10)$
$(i i) (- 6) \times (- 5) \times (- 7) \times (- 2) \times (- 3)$
$(i i i) (- 60) \times (- 10) \times (- 5) \times (- 1)$
$(i v) (- 30) \times (- 20) \times (- 5)$
$(v) (- 3) \times (- 3) \times (- 3) \times . .6$ times
$(v i) (- 5) \times (- 5) \times (- 5) \times . . .5$ times
$(v i i) (- 1) \times (- 1) \times (- 1) \times . . .200$ times
$(v i i i) (- 1) \times (- 1) \times (- 1) \times . . .171$ times

Find the mode from the given data.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2 , 3, 4, 1, 2, 3, 4, 1 ,2 , 3, 4, 5, 5, 1, 5, 5, 5, 3, 5, 1, 2, 4, 5, 6, 1, 2, 4, 2, 1

Simplify: (i) 4-1×3-12 (ii) 5-1÷6-13 (iii) 2-1+3-1-1 (iv) 3-1×4-1-1×5-1

(i) ---> (a−1 = 1/a) ---> ((a/b)n = (an)/(bn) ) =124 (ii) ---> (a−1 = 1/a) = 653 = 6353 ---> ((a/b)n = (an)/(bn) ) = 216125 (iii) (2-1+3-1)-1 =12+13-1 ---> (a−1 = 1/a) = 56-1 =15/6 ---> (a−1 = 1/a) =65 (iv) ---> (a−1 = 1/a) =125 ---> (a−1 = 1/a)

Simplify:
(i) ${(4^{- 1} \times 3^{- 1})}^{2}$
(ii) ${(5^{- 1} \div 6^{- 1})}^{3}$
(iii) ${(2^{- 1} + 3^{- 1})}^{- 1}$
(iv) ${(3^{- 1} \times 4^{- 1})}^{- 1} \times 5^{- 1}$