Question

simplify (a) {(2^-1×3^2/2^3×3^-4)}^7/2 × {(2^-2×3^3/2^3×3^-5)}-5/2​

Answer 1

Answer:

(\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

Step-by-step explanation:

Answer 2

Answer is 12

Hope it helps you...