Question

Tìm các số tự nhiên m,n biết :

a) \(\left(-\dfrac{1}{5^{ }}\right)^n\) =\(-\dfrac{1}{125}\)

b)\(\left(-\dfrac{2}{11^{ }}\right)^m=\dfrac{4}{121}\)

c)\(7^{2n}+7^{2n+2}=2450\)

Answer 1

c)\(7^{2n}+7^{2n+2}=2450\)

⇒\(7^{2n}+7^{2n}.7^2=2450\)

⇒\(7^{2n}.50=2450\)

⇒\(7^{2n}=49\)\(=7^2\)

⇒2n=2

⇒n=1

Answer 2

a)\(\left(-\dfrac{1}{5}\right)^n=-\dfrac{1}{125}\)                   b)\(\left(-\dfrac{2}{11}\right)^m=\dfrac{4}{121}\)

\(\left(-\dfrac{1}{5}\right)^n=\left(-\dfrac{1}{5}\right)^3\)                    \(=\left(-\dfrac{2}{11}\right)^m=\left(-\dfrac{2}{11}\right)^2\)

⇒n=3                                          ⇒m=2