Solve frac{6^{-10}}{81^-2*16^-3}=3^-3/3^-1

$$\frac { 6 ^ { - 10 } } { 81 ^ { - 2 } \cdot 16 ^ { - 3 } } = \frac { 3 ^ { - 3 } } { 3 ^ { - 1 } }$$

Verify

Solution Steps

Rewrite 3^{-1} as 3^{-3}\times 3^{2}. Cancel out 3^{-3} in both numerator and denominator.

$$\frac{6^{-10}}{81^{-2}\times 16^{-3}}=\frac{1}{3^{2}}$$

Calculate 6 to the power of -10 and get \frac{1}{60466176}.

$$\frac{\frac{1}{60466176}}{81^{-2}\times 16^{-3}}=\frac{1}{3^{2}}$$

Calculate 81 to the power of -2 and get \frac{1}{6561}.

$$\frac{\frac{1}{60466176}}{\frac{1}{6561}\times 16^{-3}}=\frac{1}{3^{2}}$$

Calculate 16 to the power of -3 and get \frac{1}{4096}.

$$\frac{\frac{1}{60466176}}{\frac{1}{6561}\times \frac{1}{4096}}=\frac{1}{3^{2}}$$

Multiply \frac{1}{6561} and \frac{1}{4096} to get \frac{1}{26873856}.

$$\frac{\frac{1}{60466176}}{\frac{1}{26873856}}=\frac{1}{3^{2}}$$

Divide \frac{1}{60466176} by \frac{1}{26873856} by multiplying \frac{1}{60466176} by the reciprocal of \frac{1}{26873856}.

$$\frac{1}{60466176}\times 26873856=\frac{1}{3^{2}}$$

Multiply \frac{1}{60466176} and 26873856 to get \frac{4}{9}.

$$\frac{4}{9}=\frac{1}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4}{9}=\frac{1}{9}$$

Compare \frac{4}{9} and \frac{1}{9}.

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