Question

The expression (5b3c−6)−1(5b−2a−4)−1

Answer 1

$(5b^3c^{-6})^{-1}(5b^{-2}a^{-4})^{-1}\\\\\text{use:}\ (ab)^n=a^nb^n\\\\=5^{-1}(b^3)^{-1}(c^{-6})^{-1}\cdot5^{-1}(b^{-2})^{-1}(a^{-4})^{-1}\\\\\text{use:}\ (a^n)^m=a^{nm}\ \text{and}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{1}{5}b^{-3}c^6\cdot\dfrac{1}{5}b^2a^4\\\\\text{use associative property}\ (a\cdot b)\cdot c=a\cdot(b\cdot c)\\\\=\left(\dfrac{1}{5}\cdot\dfrac{1}{5}\right)a^4(b^{-3}b^2)c^6\\\\\text{use:}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{1}{25}a^4b^{-1}c^6\\\\Answer:\\n=\dfrac{1}{25}\\\\r=4\\\\s=-1\\\\t=6$