Exponent Rules Practice Problems - Master Powers & Bases

To solve the given expression $(2^3)^6$, we apply the power of a power rule $(a^m)^n = a^{m \cdot n}$. Here, $a = 2$, $m = 3$, and $n = 6$.

Thus, we calculate the exponent:

$3 \cdot 6 = 18$

So, $(2^3)^6 = 2^{18}$.

To solve $(4^3)^2$, we use the power of a power rule which states that $(a^m)^n = a^{m \cdot n}$.

Here, $a = 4$, $m = 3$, and $n = 2$.

So, we calculate $4^{3 \cdot 2}$,

which simplifies to $4^6$.

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.

To solve this problem, let's follow these steps:

• Understand the zero exponent rule.

• Apply this rule to the given expression.

• Identify the correct answer from the given options.

According to the rule of exponents, any non-zero number raised to the power of zero is equal to $1$. This is one of the fundamental properties of exponents.
Now, apply this rule:

Step 1: We are given the expression $(-3)^0$.
Step 2: Here, $-3$ is our base. We apply the zero exponent rule, which tells us that $(-3)^0 = 1$.

Therefore, the value of $(-3)^0$ is $1$.