(81/16)^-3/4x{(9/25)^3/2divided(5/2)^-3}
Answers
Answer:
Answer:
\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}]=1(
16
81
)
4
−3
×[(
25
9
)
2
3
÷(
2
5
)
−3
]=1
Step-by-step explanation:
\left(\frac{81}{16}\right)^{\frac{-3}{4}}\times [\left(\frac{9}{25}\right)^{\frac{3}{2}}\div \left(\frac{5}{2}\right)^{-3}](
16
81
)
4
−3
×[(
25
9
)
2
3
÷(
2
5
)
−3
]
=\left(\frac{3^{4}}{2^{4}}\right)^{\frac{-3}{4}}\times \left(\frac{2^{2}}{5^{2}}\right)^{\frac{3}{2}}\times \left(\frac{5}{2}\right)^{3}=(
2
4
3
4
)
4
−3
×(
5
2
2
2
)
2
3
×(
2
5
)
3
=\left(\frac{3}{2}\right)^{4\times\frac{-3}{4}}\times \left(\frac{3}{5}\right)^{2\times \frac{3}{2}}\times \left(\frac{5}{2}\right)^{3}=(
2
3
)
4×
4
−3
×(
5
3
)
2×
2
3
×(
2
5
)
3
=\left(\frac{2}{3}\right)^{3}\times \left(\frac{3}{5}\right)^{3}\times \left(\frac{5}{2}\right)^{3}=(
3
2
)
3
×(
5
3
)
3
×(
2
5
)
3
=\left(\frac{2}{3}\times \frac{3}{5}\times \frac{5}{2}\right)^{3}=(
3
2
×
5
3
×
2
5
)
3
=1^{3}=1
3