what is -⅔×⅗+⁵/2-⅗×⅙
Answers
Answer:
HS=(
10
5
−1
×5
5
3
2
2
1
×3
3
1
×4
4
1
)÷(
4
5
−3
×6
3
3
4
×5
5
−7
)
= \Big(\frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times (2^{2})^{\frac{1}{4}}}{ (2\times5)^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \Big) \div \Big( \frac{3^{\frac{4}{3}} \times 5^{\frac{-7}{5}}}{(2^{2})^{\frac{-3}{5}} \times 2\times 3}\Big) =(
(2×5)
5
−1
×5
5
3
2
2
1
×3
3
1
×(2
2
)
4
1
)÷(
(2
2
)
5
−3
×2×3
3
3
4
×5
5
−7
)
= \Big(\frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 2^{\frac{2}{4}}}{ (2^{\frac{-1}{5}}\times5^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \Big) \div \Big( \frac{3^{\frac{4}{3}} \times 5^{\frac{-7}{5}}}{2^{\frac{-6}{5}} \times 2\times 3}\Big) =(
(2
5
−1
×5
5
−1
×5
5
3
2
2
1
×3
3
1
×2
4
2
)÷(
2
5
−6
×2×3
3
3
4
×5
5
−7
)
= \Big(\frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 2^{\frac{2}{4}}}{ (2^{\frac{-1}{5}}\times5^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \Big) \times \Big( \frac{2^{\frac{-6}{5}} \times 2\times 3}{3^{\frac{4}{3}} \times 5^{\frac{-7}{5}}}\Big) =(
(2
5
−1
×5
5
−1
×5
5
3
2
2
1
×3
3
1
×2
4
2
)×(
3
3
4
×5
5
−7
2
5
−6
×2×3
)
= 2^{\frac{1}{2}+\frac{1}{2}+\frac{1}{5}-\frac{6}{5} +1} \times 3^{\frac{1}{3} - 1 + \frac{4}{3}} \times 5^{\frac{-1}{5} + \frac{3}{5} - \frac{7}{5}}=2
2
1
+
2
1
+
5
1
−
5
6
+1
×3
3
1
−1+
3
4
×5
5
−1
+
5
3
−
5
7
= 2^{\frac{5+5+2-12+10}{10}} \times 3^{\frac{-1-3+4}{3}} \times 5^{\frac{-1+3-7}{5}} =2
10
5+5+2−12+10
×3
3
−1−3+4
×5
5
−1+3−7
\begin{gathered} = 2^{\frac{10}{10}}\times 3^{0} \times 5^{\frac{5}{5}} \\= 2\times 1 \times 5 \\= 10 \\= RHS \end{gathered}
=2
10
10
×3
0
×5
5
5
=2×1×5
=10
=RHS