Convert all the terms to base ten.

Use distribution to simplify the powers in parentheses.

On the left side, since we are multiplying powers of the same base, we can add the exponents.

Set the powers equal to each other now that the bases are similar.

Subtract  on both sides.

Divide by negative 19 on both sides.

The answer is:  

Convert the base of the right side to base four.

With common bases, the powers can be set equal to each other.

Simplify the right side.

Subtract  on both sides.

Divide by negative six on both sides.

Reduce both fractions.

The answer is:  

In order to solve this equation, we will need to change the bases of both terms.

Notice that both bases can be four raised to some power.

Replace the terms.

Set the powers equal to each other.

Divide by two on both sides.

Subtract  on both sides.

Divide by seven on both sides.

The answer is:  

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

 With same base, we can write:

 Subtract  on both sides.

 Divide  on both sides.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

 With the same base, we can write:

 Add  on both sides.

 Divide  on both sides.

Rewrite the second term in terms of base two.

Rewrite the equation.

Set the powers equal to each other.

Do NOT divide by x on both sides or we will get no solution!

Instead, subtract  from both sides.

The equation becomes:  

Divide by 255 on both sides.

The answer is:  

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

 With the same base, we can write:

 Take the square root on both sides and account for negative as well.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that . Therefore:

 Apply power rule of exponents.

 With the same base, we can now write:

 Take square root on both sides. Remember to account for negative.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 Therefore:

 With the same base, we can now write

 Subtract  on both sides.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. We don't have the same base in this case, but we do know that 

 therefore

 With the same base, we can now write:

 Subtract  on both sides.

 Divide  on both sides.