Combined Exponent Rules Practice Problems & Solutions

We use the zero exponent rule.

$X^0=1$We obtain

$112^0=1$Therefore, the correct answer is option C.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information

• Step 2: Apply the appropriate exponent rule

• Step 3: Perform the calculation

Now, let's work through each step:
Step 1: The problem gives us the expression $1^3$. This means we have a base of 1 and an exponent of 3.
Step 2: We'll use the exponentiation rule, which states that $a^n = a \times a \times \ldots \times a$ (n times).
Step 3: Since our base is 1, raising 1 to any power will still result in 1. Therefore, we can express this as $1 \times 1 \times 1 = 1$.

Therefore, the solution to $1^3$ is $1$.

To solve the problem of finding $7^0$, we will follow these steps:

• Step 1: Identify the general rule for exponents with zero.

• Step 2: Apply the rule to the given problem.

• Step 3: Consider the provided answer choices and select the correct one.

Now, let's work through each step:

Step 1: A fundamental rule in exponents is that any non-zero number raised to the power of zero is equal to one. This can be expressed as: $a^0 = 1$ where $a$ is not zero.

Step 2: Apply this rule to the problem: Since we have $7^0$, and $7$ is certainly a non-zero number, the expression evaluates to 1. Therefore, $7^0 = 1$.

Therefore, the solution to the problem is $7^0 = 1$, which corresponds to choice 2.

Let's keep in mind that the numerator and denominator of the fraction have terms with the same base, therefore we use the property of powers to divide between terms with the same base:

$\frac{b^m}{b^n}=b^{m-n}$

We apply it in the problem:

$\frac{2^4}{2^3}=2^{4-3}=2^1$

Remember that any number raised to the 1st power is equal to the number itself, meaning that:

$b^1=b$

Therefore, in the problem we obtain:

$2^1=2$

Therefore, the correct answer is option a.

Using the quotient rule for exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Here, we have $\frac{3^5}{3^2} = 3^{5-2}$

Simplifying, we get $3^3$