**How To Solve For X In Exponents With Different Bases References**. So when our bases have at least a power in common these are pretty easy to solve you get their base is the same so their exponents equal. You recall that exponents are really just repeated multiplication, so expanding them out to simple multiplication steps is one way to solve an exponent problem.

This will show you the value of the first exponential expression. Solving an exponential equation by. Multiplying exponents with different bases by the same power.

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### There Are Rules In Algebra For Simplifying Exponents With Different And Same Bases That We Can Use.

Take the logarithm of each side of the equation. Various arithmetic operations like addition, subtraction, multiplication, and division can be. Solving an exponential equation with negative exponents by taking the common log of both sides.

### You Recall That Exponents Are Really Just Repeated Multiplication, So Expanding Them Out To Simple Multiplication Steps Is One Way To Solve An Exponent Problem.

Using the powers of logarithms multiply powers 2 to the 6x equals 2 to the 4x+16, our bases are the same and so then we can just set our exponents equal 6x is equal to 4x+16, 2x is equal to 16, x is equal to 8. Isolate the exponential part of the equation. For example, consider the below multiplication;

### Solving Exponential Equations With Different Bases.

Ignore the bases, and simply set the exponents equal to each other $$ x + 1 = 9 $$ step 2. Round to the hundredths if needed. 4 x + 1 = 4 9 step 1 ignore the bases, and simply set the exponents equal to each other x + 1 = 9 step 2 solve for the variable x = 9 − 1 x = 8 check we can verify that our answer is correct by substituting.

### For Example, X Raised To The Third Power Times Y Raised To The Third Power Becomes The Product Of X Times Y Raised To The Third Power.

When adding or subtracting different bases with the same power, evaluate the exponents first, and then. Some of the law of exponent rules are below : You do not need to hit the equal key () after typing in the first exponential expression.

### Then, Solve The New Equation By Isolating The Variable On One Side.

To do this, hit the base number (large number) first, then hit the exponent. Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. The multiplication of exponent with different base and same power can be done by multiplying the base separately and then inserting the same power.