Question

4) (3/7)^2.(-7)^4

5) (-11)^12.(4/11)^6

6) (-6)^8.(5/6)^7

Answer 1

4) \(\left(\dfrac{3}{7}\right)^2\cdot\left(-7\right)^4\)

\(=\left(\dfrac{3}{7}\right)^2\cdot\left[\left(-7\right)^2\right]^2\)

\(=\left(\dfrac{3}{7}\right)^2\cdot49^2\)

\(=\left(\dfrac{3}{7}\cdot49\right)^2\)

\(=\left(\dfrac{147}{7}\right)^2\)

\(=21^2\)

\(=441\)

5) \(\left(-11\right)^{12}\cdot\left(\dfrac{4}{11}\right)^6\)

\(=\left[\left(-11\right)^2\right]^6\cdot\left(\dfrac{4}{11}\right)^6\)

\(=121^6\cdot\left(\dfrac{4}{11}\right)^6\)

\(=\left(121\cdot\dfrac{4}{11}\right)^6\)

\(=44^6\)

6) \(6^8\cdot\left(\dfrac{5}{7}\right)^7\)

\(=6^8\cdot\dfrac{5^7}{6^7}\)

\(=\dfrac{6^8\cdot5^7}{6^7}\)

\(=6\cdot5^7\)

\(=469750\)

Answer 2

\(\left(\dfrac{3}{7}\right)^2\cdot\left(-7\right)^4=\dfrac{9}{49}\cdot49^2=9\cdot49=441\)

\(\left(-11\right)^{12}\cdot\left(\dfrac{4}{11}\right)^4=11^{12}\cdot\dfrac{4^4}{11^4}=11^8\cdot4^4=54875873536\) 

\(\left(-6\right)^8\cdot\left(\dfrac{5}{6}\right)^7=6^8\cdot\dfrac{5^7}{6^7}=6\cdot5^7=469750\)