Solve [3^{8}*(3^9:3^2)^5]^-4=

$$[ 3 ^ { 8 } \cdot ( 3 ^ { 9 } : 3 ^ { 2 } ) ^ { 5 } ] ^ { - 4 } =$$

Evaluate

$$\frac{1}{11610630703530923996233764322605633554400975674804937772291047972101377433780374641}\approx 8.612796544 \cdot 10^{-83}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 9 to get 7.

$$\left(3^{8}\times \left(3^{7}\right)^{5}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$\left(3^{8}\times 3^{35}\right)^{-4}$$

To multiply powers of the same base, add their exponents. Add 8 and 35 to get 43.

$$\left(3^{43}\right)^{-4}$$

Calculate 3 to the power of 43 and get 328256967394537077627.

$$328256967394537077627^{-4}$$

Calculate 328256967394537077627 to the power of -4 and get \frac{1}{11610630703530923996233764322605633554400975674804937772291047972101377433780374641}.

$$\frac{1}{11610630703530923996233764322605633554400975674804937772291047972101377433780374641}$$

Factor

$$\frac{1}{3 ^ {172}} = 8.612796544255676 \times 10^{-83}$$