Express each o fthe following rational numbers with a negative exponent- i- 1-4 3-ii-35-iii 3-5 4-iv 3-2 4-3-iv- 7-3 4-3

(i) ( 1/4 )^3= ( 4/1 )^ 3=(4)^ 3 (ii) 3^5= ( 1/3 )^ 5 (iii) ( 3/5 )^4= ( 5/3 )^ 4 (iv){ ( 3/2 )^4}^ 3= ( 3/2 )^4 × ( 3)= ( 3/2 )^ 12 (iv) { ( 7/3 ) ^4}^ 3= ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

Express each ...

Question

Express each o fthe following rational numbers with a negative exponent:

$(i) {(\frac{1}{4})}^{3} (i i) 3^{5} (i i i) {(\frac{3}{5})}^{4} (i v) {{(\frac{3}{2})}^{4}}^{- 3} (i v) {{(\frac{7}{3})}^{4}}^{- 3}$

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Solution

$(i) {(\frac{1}{4})}^{3} = {(\frac{4}{1})}^{- 3} = (4)^{- 3} (i i) 3^{5} = {(\frac{1}{3})}^{- 5} (i i i) {(\frac{3}{5})}^{4} = {(\frac{5}{3})}^{- 4} (i v) {{(\frac{3}{2})}^{4}}^{- 3} = {(\frac{3}{2})}^{4 \times (- 3)} = {(\frac{3}{2})}^{- 12} (i v) {{(\frac{7}{3})}^{4}}^{- 3} = {(\frac{7}{3})}^{4 \times (- 3)} = {(\frac{7}{3})}^{- 12}$

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Similar questions

Q. Express each of the following rational numbers with a negative exponent:
(i)

{(\frac{1}{4})}^{3}

(ii)

3^{5}

(iii)

{(\frac{3}{5})}^{4}

(iv)

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

(v)

{\{{(\frac{7}{3})}^{4}\}}^{- 3}

Q. Express each of the following rational numbers with a positive exponent:
(i)

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

(ii)

{(\frac{5}{4})}^{- 3}

(iii)

4^{3} \times 4^{- 9}

(iv)

{\{{(\frac{4}{3})}^{- 3}\}}^{- 4}

(v)

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

Q. Simplify each of the following and express each as a rational number:

{(\frac{3}{2})}^{4} \times {(\frac{1}{5})}^{2}

Q. Express as a power of rational number with negative exponent.
(i)

{[{(\frac{- 3}{2})}^{- 2}]}^{- 3}

(ii)

(2^{5} \div 2^{8}) \times 2^{- 7}

(ii)

[{(\frac{2}{3})}^{- 3} \times {(\frac{4}{9})}^{- 1}] \div {(\frac{2}{3})}^{- 4}

Q. Express each of the following exponential expressions as a rational number.

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

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Express each o fthe following rational numbers with a negative exponent: (i) (14)3 (ii) 35 (iii)(35)4 (iv){(32)4}−3 (iv) {(73)4}−3

(i) (14)3=(41)−3=(4)−3(ii) 35=(13)−5(iii)(35)4=(53)−4(iv){(32)4}−3=(32)4×(−3)=(32)−12(iv) {(73)4}−3=(73)4×(−3)=(73)−12

Express each o fthe following rational numbers with a negative exponent:

$(i) {(\frac{1}{4})}^{3} (i i) 3^{5} (i i i) {(\frac{3}{5})}^{4} (i v) {{(\frac{3}{2})}^{4}}^{- 3} (i v) {{(\frac{7}{3})}^{4}}^{- 3}$