Powers and Roots Practice Problems - Basic Exponents

To solve this problem, we'll focus on expressing the power $2^7$ as a series of multiplications.

• Step 1: Identify the given power expression $2^7$.
• Step 2: Convert $2^7$ into a product of repeated multiplication. This involves writing 2 multiplied by itself for a total of 7 times.
• Step 3: The expanded form of $2^7$ is $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$.

By comparing this expanded form with the provided choices, we see that the correct expression is:

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

Therefore, the solution to the problem is the expression that matches this expanded multiplication form, which is the choice $\text{1: } 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$.

To solve this problem, we will apply the rule of exponents:

• Any number raised to the power of 1 remains unchanged. Therefore, by the identity property of exponents, $10,000^1 = 10,000$.

Given the choices:

• $10,000 \cdot 10,000$: This is $10,000^2$.
• $10,000 \cdot 1$: Simplifying this expression yields 10,000, which is equivalent to $10,000^1$.
• $10,000 + 10,000$: This results in 20,000, not equivalent to $10,000^1$.
• $10,000 - 10,000$: This results in 0, not equivalent to $10,000^1$.

Therefore, the correct choice is $10,000 \cdot 1$, which simplifies to 10,000, making it equivalent to $10,000^1$.

Thus, the expression $10,000^1$ is equivalent to:

$10,000 \cdot 1$

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

• Step 1: Recognize what finding a square root means
• Step 2: List known perfect squares to identify which one results in 64
• Step 3: Verify the square root by calculation

Now, let's work through each step:
Step 1: To find the square root of 64, we seek a number that, when multiplied by itself, equals 64.
Step 2: Consider the sequence of perfect squares: $1^2 = 1$, $2^2 = 4$, $3^2 = 9$, $4^2 = 16$, $5^2 = 25$, $6^2 = 36$, $7^2 = 49$, $8^2 = 64$.
Step 3: We see that $8^2 = 64$. Therefore, the square root of 64 is 8.

Therefore, the solution to this problem is $8$.

Let's solve the problem step by step:

• Step 1: Understand what the square root means.

The square root of a number $n$ is a value that, when multiplied by itself, equals $n$. This is written as $x = \sqrt{n}$.

• Step 2: Apply this definition to the number $36$.

We are looking for a number $x$ such that $x^2 = 36$. This translates to finding $x = \sqrt{36}$.

• Step 3: Determine the correct number.

We know that $6 \times 6 = 36$. Therefore, the principal square root of $36$ is $6$.

Thus, the solution to the problem is $\sqrt{36} = 6$.

Among the given choices, the correct one is: Choice 1: $6$.

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

• Step 1: Set up the multiplication as $11 \times 11$.
• Step 2: Compute the product using basic arithmetic.
• Step 3: Compare the result with the provided multiple-choice answers to identify the correct one.

Now, let's work through each step:
Step 1: We begin with the calculation $11 \times 11$.
Step 2: Perform the multiplication:

1. Multiply the units digits: $1 \times 1 = 1$.
2. Next, for the tens digits: $11 \times 10 = 110$.
3. Add the results: $110 + 1 = 111$. This doesn't seem right, so let's break it down further.

Let's examine a more structured multiplication method:

Multiply $11$ by $1$ (last digit of the second 11), we get 11.
Multiply $11$ by $10$ (tens place of the second 11), we get 110.

If we align correctly and add the partial products:

11
+ 110
------------
121

Step 3: The correct multiplication yields the final result as $121$. Upon reviewing the provided choices, the correct answer is choice 4: $121$.

Therefore, the solution to the problem is $121$.