Solve frac{(3)^{5}(3)^2(-3)^4}{(3)(3)^8}=3^2=9

$$\frac { ( 3 ) ^ { 5 } ( 3 ) ^ { 2 } ( - 3 ) ^ { 4 } } { ( 3 ) ( 3 ) ^ { 8 } } = 3 ^ { 2 } = 9$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{3^{7}\left(-3\right)^{4}}{3\times 3^{8}}=3^{2}\text{ and }3^{2}=9$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\frac{3^{7}\left(-3\right)^{4}}{3^{9}}=3^{2}\text{ and }3^{2}=9$$

Cancel out 3^{7} in both numerator and denominator.

$$\frac{\left(-3\right)^{4}}{3^{2}}=3^{2}\text{ and }3^{2}=9$$

Calculate -3 to the power of 4 and get 81.

$$\frac{81}{3^{2}}=3^{2}\text{ and }3^{2}=9$$

Calculate 3 to the power of 2 and get 9.

$$\frac{81}{9}=3^{2}\text{ and }3^{2}=9$$

Divide 81 by 9 to get 9.

$$9=3^{2}\text{ and }3^{2}=9$$

Calculate 3 to the power of 2 and get 9.

$$9=9\text{ and }3^{2}=9$$

Compare 9 and 9.

$$\text{true}\text{ and }3^{2}=9$$

Calculate 3 to the power of 2 and get 9.

$$\text{true}\text{ and }9=9$$

Compare 9 and 9.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$