Solve 2^7/2^5=3^-5/3^-2

$$\frac { 2 ^ { 7 } } { 2 ^ { 5 } } = \frac { 3 ^ { - 5 } } { 3 ^ { - 2 } }$$

Verify

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$2^{2}=\frac{3^{-5}}{3^{-2}}$$

Rewrite 3^{-2} as 3^{-5}\times 3^{3}. Cancel out 3^{-5} in both numerator and denominator.

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 3 and get 27.

$$4=\frac{1}{27}$$

Convert 4 to fraction \frac{108}{27}.

$$\frac{108}{27}=\frac{1}{27}$$

Compare \frac{108}{27} and \frac{1}{27}.

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