Simplify [5(8⅓+27⅓)³]¼
Answers
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