Simplify 9^1/3×27^1/2÷3^-1/6×3^1/3
Answers
Answer:
(3)^2×1/3×3^3×1/2÷3-1/6×3^1/3
3^2/3×3^3/2÷3-1/6×3^1/3
as base same we work on power
3^2/3+3/2÷3^-1/6+1/3
= 3^13/6÷3^1/6
=3^13/6-1/6
3^12 using x^n÷x^m=x^n-m
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Step-by-step explanation:
Answer:
\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}=3^{\frac{-1}{3}}
3
6
1
×3
−
3
2
9
3
1
×27
−
2
1
=3
3
−1
Step-by-step explanation:
Given Expression: \frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}
3
6
1
×3
−
3
2
9
3
1
×27
−
2
1
We have to simplify it,
Consider,
\frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}
3
6
1
×3
−
3
2
9
3
1
×27
−
2
1
\implies\frac{(3^2)^{\frac{1}{3}}\times(3^3)^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹
3
6
1
×3
−
3
2
(3
2
)
3
1
×(3
3
)
−
2
1
Now we use law of exponent, (x^a)^b=x^{a\times b}(x
a
)
b
=x
a×b
\implies\frac{3^{2\times{\frac{1}{3}}}\times3^{3\times{-\frac{1}{2}}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹
3
6
1
×3
−
3
2
3
2×
3
1
×3
3×−
2
1
\implies\frac{3^{\frac{2}{3}}\times3^{\frac{-3}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}⟹
3
6
1
×3
−
3
2
3
3
2
×3
2
−3
We use another law of exponent, x^a\times x^b=x^{a+b}x
a
×x
b
=x
a+b
\implies\frac{3^{\frac{2}{3}+\frac{-3}{2}}}{3^{\frac{1}{6}+(-\frac{2}{3})}}⟹
3
6
1
+(−
3
2
)
3
3
2
+
2
−3
\implies\frac{3^{\frac{-5}{6}}}{3^{\frac{-1}{2}}}⟹
3
2
−1
3
6
−5
We use another law of exponent, \frac{x^a}{x^b}=x^{a-b}
x
b
x
a
=x
a−b
\implies3^{\frac{-5}{6}-\frac{-1}{2}}⟹3
6
−5
−
2
−1
\implies3^{\frac{-1}{3}}⟹3
3
−1
Therefore, \frac{9^{\frac{1}{3}}\times27^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times3^{-\frac{2}{3}}}=3^{\frac{-1}{3}}
3
6
1
×3
−
3
2
9
3
1
×27
−
2
1
=3
3
−1