Simple Exponents - Algebra 2

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

We know that .

Remember when having negative exponents

which is the positive exponent raising base .

Therefore

.

Remember to apply the power rule of exponents.

The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since . The largest can be found by noting that ; this makes the greatest perfect square in this range.

Since the squares of the integers from 10 to 31 all fall in this range, this makes perfect squares.

Solve for x:

Step 1: Represent exponentially with a base of

, therefore

Step 2: Set the exponents equal to each other and solve for x

Rewrite in exponential form with a base of :

Solve for by equating exponents:

Represent in exponential form using a base of :

Solve for by equating exponents:

To solve this expression, remove the outer exponent and expand the terms.

By exponential rules, add all the powers when multiplying like terms.

The answer is:

The first step in solving for x is to simplify the right side:

.

Next, we can re-express the left side as an exponential with 2 as the base.

Now set the new left side equal to the new right side.

With the bases now being the same, we can simply set the exponents equal to each other.

To solve for x, we need to simplify both sides in order to make the equation simpler to solve.

can be rewritten as , and can be written as .

Setting the two sides equal to each other gives us

Since the bases are the same we can set the exponents equal to each other.

When we expand exponents, we simply repeat the base by the exponential value.

Therefore:

When we expand exponents, we simply repeat the base by the exponential value.

Therefore:

is expanded to .

We will simply multiply the values in order to get the answer:

is expanded to .

We will simply multiply the values in order to get the answer:

When exponents are negative, we can express them usinf the following format:

in this formula, is a positive exponent and is the base.

We can express as , which is also the same as:

When exponents are negative, we can express them usinf the following format:

in this formula, is a positive exponent and is the base.

Therefore:

When adding exponents, we first need to factor common terms.

Let's start by factoring out the following:

Factor.