[frac{(f^{3}g^{-8}h)^{7}}{(g^5h^-3f)^-8}]^5 eching

$$[ \frac { ( f ^ { 3 } g ^ { - 8 } h ) ^ { 7 } } { ( g ^ { 5 } h ^ { - 3 } f ) ^ { - 8 } } ] ^ { 5 }$$

Baholash

$$\frac{f^{145}}{g^{80}h^{85}}$$

Yechim qadamlari

\left(f^{3}g^{-8}h\right)^{7} ni kengaytirish.

$$\left(\frac{\left(f^{3}\right)^{7}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 7 ni ko‘paytirib, 21 ni oling.

$$\left(\frac{f^{21}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -8 va 7 ni ko‘paytirib, -56 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

\left(g^{5}h^{-3}f\right)^{-8} ni kengaytirish.

$$\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}\right)^{-8}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va -8 ni ko‘paytirib, -40 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -3 va -8 ni ko‘paytirib, 24 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}h^{24}f^{-8}}\right)^{5}$$

Surat va maxrajdagi ikkala h^{7} ni qisqartiring.

$$\left(\frac{g^{-56}f^{21}}{g^{-40}f^{-8}h^{17}}\right)^{5}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\left(\frac{g^{-56}f^{29}}{g^{-40}h^{17}}\right)^{5}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\left(\frac{f^{29}}{g^{16}h^{17}}\right)^{5}$$

\frac{f^{29}}{g^{16}h^{17}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(f^{29}\right)^{5}}{\left(g^{16}h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 29 va 5 ni ko‘paytirib, 145 ni oling.

$$\frac{f^{145}}{\left(g^{16}h^{17}\right)^{5}}$$

\left(g^{16}h^{17}\right)^{5} ni kengaytirish.

$$\frac{f^{145}}{\left(g^{16}\right)^{5}\left(h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 16 va 5 ni ko‘paytirib, 80 ni oling.

$$\frac{f^{145}}{g^{80}\left(h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 17 va 5 ni ko‘paytirib, 85 ni oling.

$$\frac{f^{145}}{g^{80}h^{85}}$$

Kengaytirish

$$\frac{f^{145}}{g^{80}h^{85}}$$

Yechim qadamlari

\left(f^{3}g^{-8}h\right)^{7} ni kengaytirish.

$$\left(\frac{\left(f^{3}\right)^{7}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 7 ni ko‘paytirib, 21 ni oling.

$$\left(\frac{f^{21}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -8 va 7 ni ko‘paytirib, -56 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}$$

\left(g^{5}h^{-3}f\right)^{-8} ni kengaytirish.

$$\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}\right)^{-8}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va -8 ni ko‘paytirib, -40 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -3 va -8 ni ko‘paytirib, 24 ni oling.

$$\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}h^{24}f^{-8}}\right)^{5}$$

Surat va maxrajdagi ikkala h^{7} ni qisqartiring.

$$\left(\frac{g^{-56}f^{21}}{g^{-40}f^{-8}h^{17}}\right)^{5}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\left(\frac{g^{-56}f^{29}}{g^{-40}h^{17}}\right)^{5}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\left(\frac{f^{29}}{g^{16}h^{17}}\right)^{5}$$

\frac{f^{29}}{g^{16}h^{17}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(f^{29}\right)^{5}}{\left(g^{16}h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 29 va 5 ni ko‘paytirib, 145 ni oling.

$$\frac{f^{145}}{\left(g^{16}h^{17}\right)^{5}}$$

\left(g^{16}h^{17}\right)^{5} ni kengaytirish.

$$\frac{f^{145}}{\left(g^{16}\right)^{5}\left(h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 16 va 5 ni ko‘paytirib, 80 ni oling.

$$\frac{f^{145}}{g^{80}\left(h^{17}\right)^{5}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 17 va 5 ni ko‘paytirib, 85 ni oling.

$$\frac{f^{145}}{g^{80}h^{85}}$$