Whakaoti i te sqrt[2]{sqrt[3]{64}}=2^n/m

$$\sqrt[ 2 ] { \sqrt[ 3 ] { 64 } } = 2 ^ { n / m }$$

Whakaoti mō n

$$n=m$$

$$m\neq 0$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Tātaitia te \sqrt[3]{64} kia tae ki 4.

$$\sqrt[2]{4}=2^{\frac{n}{m}}$$

Tātaitia te \sqrt[2]{4} kia tae ki 2.

$$2=2^{\frac{n}{m}}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2^{\frac{n}{m}}=2$$

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$2^{\frac{1}{m}n}=2$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(2^{\frac{1}{m}n})=\log(2)$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$\frac{1}{m}n\log(2)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(2).

$$\frac{1}{m}n=\frac{\log(2)}{\log(2)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$\frac{1}{m}n=\log_{2}\left(2\right)$$

Whakawehea ngā taha e rua ki te m^{-1}.

$$n=\frac{m}{1}$$

Whakaoti mō m

$$m=n$$

$$n\neq 0$$