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\left(\frac{\left(f^{3}\right)^{7}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
Expand \left(f^{3}g^{-8}h\right)^{7}.
\left(\frac{f^{21}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.
\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply -8 and 7 to get -56.
\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}\right)^{-8}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}
Expand \left(g^{5}h^{-3}f\right)^{-8}.
\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply 5 and -8 to get -40.
\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}h^{24}f^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply -3 and -8 to get 24.
\left(\frac{g^{-56}f^{21}}{g^{-40}f^{-8}h^{17}}\right)^{5}
Cancel out h^{7} in both numerator and denominator.
\left(\frac{g^{-56}f^{29}}{g^{-40}h^{17}}\right)^{5}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(\frac{f^{29}}{g^{16}h^{17}}\right)^{5}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{\left(f^{29}\right)^{5}}{\left(g^{16}h^{17}\right)^{5}}
To raise \frac{f^{29}}{g^{16}h^{17}} to a power, raise both numerator and denominator to the power and then divide.
\frac{f^{145}}{\left(g^{16}h^{17}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 29 and 5 to get 145.
\frac{f^{145}}{\left(g^{16}\right)^{5}\left(h^{17}\right)^{5}}
Expand \left(g^{16}h^{17}\right)^{5}.
\frac{f^{145}}{g^{80}\left(h^{17}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 16 and 5 to get 80.
\frac{f^{145}}{g^{80}h^{85}}
To raise a power to another power, multiply the exponents. Multiply 17 and 5 to get 85.
\left(\frac{\left(f^{3}\right)^{7}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
Expand \left(f^{3}g^{-8}h\right)^{7}.
\left(\frac{f^{21}\left(g^{-8}\right)^{7}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.
\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}h^{-3}f\right)^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply -8 and 7 to get -56.
\left(\frac{f^{21}g^{-56}h^{7}}{\left(g^{5}\right)^{-8}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}
Expand \left(g^{5}h^{-3}f\right)^{-8}.
\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}\left(h^{-3}\right)^{-8}f^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply 5 and -8 to get -40.
\left(\frac{f^{21}g^{-56}h^{7}}{g^{-40}h^{24}f^{-8}}\right)^{5}
To raise a power to another power, multiply the exponents. Multiply -3 and -8 to get 24.
\left(\frac{g^{-56}f^{21}}{g^{-40}f^{-8}h^{17}}\right)^{5}
Cancel out h^{7} in both numerator and denominator.
\left(\frac{g^{-56}f^{29}}{g^{-40}h^{17}}\right)^{5}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(\frac{f^{29}}{g^{16}h^{17}}\right)^{5}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{\left(f^{29}\right)^{5}}{\left(g^{16}h^{17}\right)^{5}}
To raise \frac{f^{29}}{g^{16}h^{17}} to a power, raise both numerator and denominator to the power and then divide.
\frac{f^{145}}{\left(g^{16}h^{17}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 29 and 5 to get 145.
\frac{f^{145}}{\left(g^{16}\right)^{5}\left(h^{17}\right)^{5}}
Expand \left(g^{16}h^{17}\right)^{5}.
\frac{f^{145}}{g^{80}\left(h^{17}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 16 and 5 to get 80.
\frac{f^{145}}{g^{80}h^{85}}
To raise a power to another power, multiply the exponents. Multiply 17 and 5 to get 85.