Math, asked by Harsin, 4 months ago

Simplify [5(8⅓+27⅓)³]¼​

Answers

Answered by MohitKumarJangra
1

Answer:

y=5

PREMISES

y=[5(8^1/3+27^1/3)^3]^1/4

CALCULATIONS

y=[5(8^1/3+27^1/3)^3]^1/4

y=[5(2+3)^3]^1/4 (Calculate the third-root of the two terms in the parens 8 and 27)

y=[5(5)^3)]^1/4 (Calculate the third-power of 5)

y=[5(125)]^1/4

y=(625)^1/4 (Take the fourth-root of 625)

y=

5

PROOF

If y=5, then the inverse of the expression [5(8^1/3+27^1/3)^3]^1/4 returns

y^4=[5(8^1/3+27^1/3)^3]

5^4=[5(8^1/3+27^1/3)^3]

5^4=[5(2+3)^3]

5^4=(5^1)(5)^3)

5^4=5^(1+3)

5^4=5^4 and

625=625 establishes the solution y=5 to the expression [5(8^1/3+27^1/3)^3]^1/4

C.H.

Step-by-step explanation:

[5(813+2713)3]14

Parentheses first

Exponents (ie Powers and Square Roots, etc.)

Multiplication and Division (left-to-right)

Addition and Subtraction (left-to-right)

Order of Operations

Note that

abc=ab−−√c=(a−−√c)b

a=a1

ab⋅ac=ab+c

a(b)≡a×b

So let’s get on track:

[5(813+2713)3]14=

5(8–√3+27−−√3)3−−−−−−−−−−−−√4=

5(2+27−−√3)3−−−−−−−−−−√4=

5(2+3)3−−−−−−−√4=

5(5)3−−−−√4=

54−−√4=

5

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