Solve 4^2*4^9*4^-12=4^2+9-12={4}^-1

$${ 4 }^{ 2 } \times { 4 }^{ 9 } \times { 4 }^{ -12 } = { 4 }^{ 2+9-12 } = { 4 }^{ -1 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$4^{11}\times 4^{-12}=4^{2+9-12}\text{ and }4^{2+9-12}=4^{-1}$$

To multiply powers of the same base, add their exponents. Add 11 and -12 to get -1.

$$4^{-1}=4^{2+9-12}\text{ and }4^{2+9-12}=4^{-1}$$

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

$$\frac{1}{4}=4^{2+9-12}\text{ and }4^{2+9-12}=4^{-1}$$

Add 2 and 9 to get 11.

$$\frac{1}{4}=4^{11-12}\text{ and }4^{2+9-12}=4^{-1}$$

Subtract 12 from 11 to get -1.

$$\frac{1}{4}=4^{-1}\text{ and }4^{2+9-12}=4^{-1}$$

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

$$\frac{1}{4}=\frac{1}{4}\text{ and }4^{2+9-12}=4^{-1}$$

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

$$\text{true}\text{ and }4^{2+9-12}=4^{-1}$$

Add 2 and 9 to get 11.

$$\text{true}\text{ and }4^{11-12}=4^{-1}$$

Subtract 12 from 11 to get -1.

$$\text{true}\text{ and }4^{-1}=4^{-1}$$

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

$$\text{true}\text{ and }\frac{1}{4}=4^{-1}$$

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

$$\text{true}\text{ and }\frac{1}{4}=\frac{1}{4}$$

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

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

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

$$\text{true}$$