(v) (3/5) ^ 4 * (3/5) ^ 3 * (3/5) ^ 8
Answers
(
5
3
)
4
×(
5
8
)
−12
×(
5
32
)
6
=
2
6
3
4
×5
2
Step-by-step explanation:
\left(\frac{3}{5}\right)^{4}\times \left(\frac{8}{5}\right)^{-12}\times\left(\frac{32}{5}\right)^{6}(
5
3
)
4
×(
5
8
)
−12
×(
5
32
)
6
=\left(\frac{3}{5}\right)^{4}\times \left(\frac{2^{3}}{5}\right)^{-12}\times\left(\frac{2^{5}}{5}\right)^{6}=(
5
3
)
4
×(
5
2
3
)
−12
×(
5
2
5
)
6
=\left(\frac{3}{5}\right)^{4}\times \left(\frac{5}{2^{3}}\right)^{12}\times\left(\frac{2^{5}}{5}\right)^{6}=(
5
3
)
4
×(
2
3
5
)
12
×(
5
2
5
)
6
\begin{gathered}By\: Exponential \:laws:\\ < /p > < p > i) \left(\frac{x}{y}\right)^{-n}=\left(\frac{y}{x}\right)^{n}\end{gathered}
ByExponentiallaws:
</p><p>i)(
y
x
)
−n
=(
x
y
)
n
ii)\left(\frac{x}{y}\right)^{n}=\frac{x^{n}}{y^{n}}ii)(
y
x
)
n
=
y
n
x
n
iii)\frac{x^{m}}{x^{n}}=x^{m-n}=\frac{1}{x^{n-m}}iii)
x
n
x
m
=x
m−n
=
x
n−m
1
iv)x^{m}\times x^{n}=x^{m+n}iv)x
m
×x
n
=x
m+n
v)(x^{m})^{n}=x^{mn}v)(x
m
)
n
=x
mn
=\frac{3^{4}}{5^{4}}\times\frac{5^{12}}{2^{36}}\times \frac{2^{30}}{5^{6}}=
5
4
3
4
×
2
36
5
12
×
5
6
2
30
=\frac{3^{4}\times 5^{12-4-6}}{2^{36-30}}=
2
36−30
3
4
×5
12−4−6
=\frac{3^{4}\times 5^{2}}{2^{6}}=
2
6
3
4
×5
2
Therefore,
\begin{gathered}\left(\frac{3}{5}\right)^{4}\times \left(\frac{8}{5}\right)^{-12}\times\left(\frac{32}{5}\right)^{6}\\=\frac{3^{4}\times 5^{2}}{2^{6}}\end{gathered}
(
5
3
)
4
×(
5
8
)
−12
×(
5
32
)
6
=
2
6
3
4
×5
2