Real Exponents - College Algebra

When like bases with exponents are multiplied, the value of the product's exponent is the sum of both original exponents as shown here:

We can use this common rule to solve for in the practice problem:

The product of dividing like bases with exponents is the difference of the numerator and denominator exponents. This is a common rule when working with rational exponents:

We can use this common rule to solve for :

To solve for , we need all values to have like bases:

Now that all values have like bases, we can solve for :

To solve for , we want all values in the equation to have like bases:

Now we can solve for :

To solve for , we want all the values in the equation to have like bases:

Now we can solve for :

When multiplying exponential, the exponents always add. While the 2 in the front of the first exponential might throw you off, you may disregard it initially.

Which simplifies to

Our final answer is

First, we need to simplify the numerator. First term, can be simplified to . Plugging this back into the numerator, we get

, which simplifies to . Plugging this back into the original equation gives us

, which is simply .

The original expression can be rewritten as

. Whenever you can a fraction raised to a power, that power gets distributed out to the numerator and denominator. In mathematical terms, the new expression is

, which simply becomes , or

Treat this with regular exponent rules.

When like bases with exponents are multiplied, the value of the product's exponent is the sum of both original exponents as shown here:

We can use this common rule to solve for in the practice problem:

The product of dividing like bases with exponents is the difference of the numerator and denominator exponents. This is a common rule when working with rational exponents:

We can use this common rule to solve for :

To solve for , we need all values to have like bases:

Now that all values have like bases, we can solve for :

To solve for , we want all values in the equation to have like bases:

Now we can solve for :

To solve for , we want all the values in the equation to have like bases:

Now we can solve for :

When multiplying exponential, the exponents always add. While the 2 in the front of the first exponential might throw you off, you may disregard it initially.

Which simplifies to

Our final answer is

First, we need to simplify the numerator. First term, can be simplified to . Plugging this back into the numerator, we get

, which simplifies to . Plugging this back into the original equation gives us

, which is simply .

The original expression can be rewritten as

. Whenever you can a fraction raised to a power, that power gets distributed out to the numerator and denominator. In mathematical terms, the new expression is

, which simply becomes , or