Problem 25 Evaluate each exponential. $$ ... [FREE SOLUTION]

Chapter 7: Problem 25

Evaluate each exponential. $$ 100^{3 / 2} $$

Short Answer

Expert verified

1000

Step by step solution

- Understand the Exponential Form

To evaluate the exponential expression, identify the base and the exponent. Here, the base is 100 and the exponent is $\frac{3}{2}$.

- Rewrite the Exponent

Rewrite the exponent $\frac{3}{2}$ as a combination of a square root and a power. This means: $100^{3/2} = (100^{1/2})^3$.

- Calculate the Square Root

Calculate $100^{1/2}$. This is the same as finding the square root of 100. $\sqrt{100} = 10$.

- Raise to the Power of 3

Now, take the result from the previous step (which is 10) and raise it to the power of 3. $10^3 = 10 \times 10 \times 10 = 1000$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

exponential form

Exponential form is a way to express repeated multiplication of a number by itself. In our exercise, we are given the expression $100^{3 / 2}$. Here, '100' is the base, and $\frac{3}{2}$ is the exponent.

The base is the number that is being multiplied repeatedly, while the exponent tells us how many times to multiply the base by itself. When the exponent is a fraction, it can represent both a power and a root, which makes it a bit more complex.

For example, in $100^{3/2}$, the fraction $\frac{3}{2}$ indicates that we need to find a combination of a square root and a power. This leads us to the next core concept.

square root

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the expression $100^{3/2}$, we need to find the square root of 100 before raising it to the power of 3.

The square root of 100 is calculated as follows: $\sqrt{100} = 10$.

This is because 10 multiplied by itself (10 x 10) equals 100. So, we have simplified our expression to $10^3$. Now, we move on to applying the power.

power and exponents

Powers and exponents are fundamental concepts that allow us to express large numbers in a compact form.

As seen in the last step, we simplified our problem to $10^3$. This means we need to multiply the base (10) by itself three times:

$10^3 = 10 \times 10 \times 10$.

Performing the multiplication, we get $1000$. Therefore, the value of $100^{3 / 2}$ is 1000.

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91影视

Evaluate each exponential. $$ 100^{3 / 2} $$

Short Answer

Step by step solution

- Understand the Exponential Form

- Rewrite the Exponent

- Calculate the Square Root

- Raise to the Power of 3

Key Concepts

exponential form

square root

power and exponents

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