# Using exponents to solve problems

What’s $34^{23}$? If you’re scrambling to answer that question then you should probably review on how power and exponents work. $34^{23}$ is simply equal to 34 multiplied to 34 23 times. Power is consisted of a base and an exponent which is in our case is 34 and 23 respectively. A Power is the easiest way to express mathematical expression that involves multiplying a number to itself by a certain number of times. In 3.1 we will be taught how to transform strips of number into its exponential form.

Like in every mathematical operation, there are rules to follow. In this chapter we will be discussing the different exponent rules. Knowing and understanding each of these would enable us to solve problems involving exponents.

In 3.2, we will get to look at them closer and use these rules to answer math problems. Among the rules are rules we are to discuss in 3.2 is that we need to simplify exponents. If for example you are given ($25^{2}$)($25^{3}$), where you have the same bases but different exponents multiplied to one another, then you will need to add the exponents. This would stay true for all other expressions given that the powers have the same bases.

Now if the expression looks like this: ($25^{2})^3$, where the power is raised to another power, you will simply multiply the two exponents and use that as the final exponent to get $25^{6}$. The same as through if there only variables inside the parenthesis, like ($x^{2})^5$, this would be equal to $x^{6}$.

If there are two terms in the expression that are to be multiplied say for example ($25x^{2})^3$ then you will distribute the exponent found outside to all the terms inside the parenthesis, so that would be: $25^{3}x^{6}$. Bear in mind though that his rule is only applicable if the operation inside the parenthesis is multiplication.

Don’t get confused if the terms inside the parenthesis are to be added because instead of distributing the exponent to the terms you are to translate the equation according to the exponent given. If you were given ($25-x)^{3}$ then this means that you are to multiply 25-x to itself three times. If you’re given ($x + y)^2$ then that means you need to square x+y.

Another rule states that any number raised to 0 will be equal to one. So if you’re given $1000000^{0}$ then you should know that it would always be 1.

In the event that the exponents are in fractional form, you should review what we have learned about fractions previously to fully understand how to simplify these kinds of exponents.

After learning all the rules we can then move to 3.3 where we will get to understand the order of operations with exponents. Then in 3.4 we will use all the rules we learned to solve problems.

### Using exponents to solve problems

In this section, you will try to apply what we learn about exponents in the previous sections to solve word problems such as, calculating the volume of a cube, and more.