Evaluate- - 5 81-3 -271-33-1-4

#160; #160; [ 5( 8^1/3 +27^1/3)^3]^14 =[ 5( 2^3/3 +3^3/3)^3 #160;]^14 =[ 5( 5)^3 #160;]^14 =[ 5^4 ]^14 =(5)^44 =5 ...

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Byju's Answer

Standard IX

Mathematics

Exponential Representation for Irrational Numbers

Evaluate: [ ...

Question

Evaluate:
${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$

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Solution

${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$
$= {[5 {(2^{\frac{3}{3}} + 3^{\frac{3}{3}})}^{3}]}^{\frac{1}{4}}$
$= {[5 {(5)}^{3}]}^{\frac{1}{4}}$
$= {[5^{4}]}^{\frac{1}{4}}$
$= (5)^{\frac{4}{4}}$
$= 5$

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Similar questions

Q. Simplify :

{[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}

Evaluate (i) $(1^{3} + 2^{3} + 3^{3})^{\frac{1}{2}}$ (ii) ${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$ (iii) $\frac{2^{0} + 7^{0}}{5^{0}}$ (iv) ${[(16)^{\frac{1}{2}}]}^{\frac{1}{2}}$

Q. Fill in the blanks

{(\begin{matrix} 5 (8^{1 / 3} + 27^{1 / 3})^{3} \end{matrix})}^{1 / 4} =

_____.

Q. Evaluate

{⎡ ⎢ ⎣ 7 (64^{\frac{1}{3}} + 27^{\frac{1}{3}})^{3} ⎤ ⎥ ⎦}^{\frac{1}{4}}

Q. Find the value of the following

a) [5 (8^{\frac{1}{3}} + 27^{\frac{1}{3}})^{3}]^{\frac{1}{4}}

b) (0.000064)^{\frac{5}{4}} \times (0.04)^{\frac{5}{4}}

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Evaluate:[5(813+2713)3]14

[5(813+2713)3]14=[5(233+333)3]14=[5(5)3]14=[54]14=(5)44=5

Evaluate:
${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$

${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$
$= {[5 {(2^{\frac{3}{3}} + 3^{\frac{3}{3}})}^{3}]}^{\frac{1}{4}}$
$= {[5 {(5)}^{3}]}^{\frac{1}{4}}$
$= {[5^{4}]}^{\frac{1}{4}}$
$= (5)^{\frac{4}{4}}$
$= 5$