Question

Simplify ((5^-1×7^2)/(5^2×7^-4))^7/2×((5^-2×7^3)/(5^3×7-5))^-5/2

Answer 1

See Attachment......

Answer 2

Answer:

The answer is 175.

Step-by-step explanation:

$(\frac{5^{-1}\times 7^2}{5^2\times 7^{-4}})^\frac{7}{2}\times (\frac{5^{-2}\times 7^3}{5^3\times 7^{-5}})^{-\frac{5}{2}}$

$(\frac{a^m}{a^n}=a^{m-n})$

$=(5^{-1+2}\times 7^{2+4})^\frac{7}{2}\times (5^{-2-3}\times 7^{3+5})^{-\frac{5}{2}}$

$=(5^{-3}\times 7^6)^\frac{7}{2}\times (5^{-5}\times 7^8)^{-\frac{5}{2}}$

$=5^{-\frac{21}{2}}\times 7^{\frac{42}{2}}\times 5^{\frac{25}{2}}\times 7^{-\frac{40}{2}}$

$((a^m)^n=a^{m\times n})$

$=5^{\frac{-21+25}{2}}\times 7^{\frac{42-40}{2}}$

$(a^m.a^n=a^{m+n})$

$=5^{\frac{4}{2}}\times 7^{\frac{2}{2}}$

$=5^2\times 7^1$

$=25\times 7$

$=175$