Solve 3^2*3^-8=3/3^8

$$3 ^ { 2 } \cdot 3 ^ { - 8 } = \frac { 3 } { 3 ^ { 8 } }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -8 to get -6.

$$3^{-6}=\frac{3}{3^{8}}$$

Rewrite 3^{8} as 3\times 3^{7}. Cancel out 3 in both numerator and denominator.

$$3^{-6}=\frac{1}{3^{7}}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{1}{729}=\frac{1}{3^{7}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{1}{729}=\frac{1}{2187}$$

Least common multiple of 729 and 2187 is 2187. Convert \frac{1}{729} and \frac{1}{2187} to fractions with denominator 2187.

$$\frac{3}{2187}=\frac{1}{2187}$$

Compare \frac{3}{2187} and \frac{1}{2187}.

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