Question

simplify....... (3/5)^4 (8/5)^-12 (32/5)^6

Answer 1

Answer:

$\left(\frac{3}{5}\right)^{4}\times \left(\frac{8}{5}\right)^{-12}\times\left(\frac{32}{5}\right)^{6}\\=\frac{3^{4}\times 5^{2}}{2^{6}}$

Step-by-step explanation:

$\left(\frac{3}{5}\right)^{4}\times \left(\frac{8}{5}\right)^{-12}\times\left(\frac{32}{5}\right)^{6}$

$=\left(\frac{3}{5}\right)^{4}\times \left(\frac{2^{3}}{5}\right)^{-12}\times\left(\frac{2^{5}}{5}\right)^{6}$

$=\left(\frac{3}{5}\right)^{4}\times \left(\frac{5}{2^{3}}\right)^{12}\times\left(\frac{2^{5}}{5}\right)^{6}$

$By\: Exponential \:laws:\\</p><p>i) \left(\frac{x}{y}\right)^{-n}=\left(\frac{y}{x}\right)^{n}$

$ii)\left(\frac{x}{y}\right)^{n}=\frac{x^{n}}{y^{n}}$

$iii)\frac{x^{m}}{x^{n}}=x^{m-n}=\frac{1}{x^{n-m}}$

$iv)x^{m}\times x^{n}=x^{m+n}$

$v)(x^{m})^{n}=x^{mn}$

$=\frac{3^{4}}{5^{4}}\times\frac{5^{12}}{2^{36}}\times \frac{2^{30}}{5^{6}}$

$=\frac{3^{4}\times 5^{12-4-6}}{2^{36-30}}$

$=\frac{3^{4}\times 5^{2}}{2^{6}}$

Therefore,

$\left(\frac{3}{5}\right)^{4}\times \left(\frac{8}{5}\right)^{-12}\times\left(\frac{32}{5}\right)^{6}\\=\frac{3^{4}\times 5^{2}}{2^{6}}$

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Answer 2

Answer:

hope it helped thanking you