The problem is a worksheet about exponents. It includes writing numbers in exponential form, expanded form, and standard form. It also asks to identify the base of a number and solve some related problems.

1. Problem Description

The problem is a worksheet about exponents. It includes writing numbers in exponential form, expanded form, and standard form. It also asks to identify the base of a number and solve some related problems.

2. Solution Steps

1. Write $5 \times 5 \times 5 \times 5 \times 5 \times 5$ in exponential form.

Since 5 is multiplied by itself 6 times, the exponential form is $5^6$.

2. Write $7^4$ in expanded form.

$7^4$ means 7 multiplied by itself 4 times, so the expanded form is $7 \times 7 \times 7 \times 7$.

3. Write each number below in standard form.

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

$3^3 = 3 \times 3 \times 3 = 27$

$11^2 = 11 \times 11 = 121$

$4^3 = 4 \times 4 \times 4 = 64$

4. Write the base of each number.

The base of $8^7$ is

8. The base of $7^9$ is

7. The base of $25^{10}$ is

2

5. The base of $12^4$ is

1

2.

5. If you write $14^6$ in expanded form, how many factors will there be?

$14^6$ means 14 multiplied by itself 6 times. Therefore, there are 6 factors.

6. What number equals 100 when it is squared?

We are looking for a number $x$ such that $x^2 = 100$. Since $10 \times 10 = 100$, the number is

1

0.

7. What number equals 8 when it is cubed?

We are looking for a number $x$ such that $x^3 = 8$. Since $2 \times 2 \times 2 = 8$, the number is

2.

8. What is the sum of $2^4$ and $7^2$? Write the answer in standard form.

$2^4 = 2 \times 2 \times 2 \times 2 = 16$

$7^2 = 7 \times 7 = 49$

$16 + 49 = 65$

9. Write the following expression in exponential form: $8 \times 8 \times 8 \times 8 \times 3 \times 3$

The expression can be written as $8^4 \times 3^2$.

1

0. Write the following expression in expanded form: $9^3 \times 7^3$

$9^3 = 9 \times 9 \times 9$

$7^3 = 7 \times 7 \times 7$

So, $9^3 \times 7^3 = (9 \times 9 \times 9) \times (7 \times 7 \times 7)$.

3. Final Answer

1. $5^6$

2. $7 \times 7 \times 7 \times 7$

3. 32, 27, 121, 64

4. 8, 7, 25, 12

5. 6

6. 10

7. 2

8. 65

9. $8^4 \times 3^2$

1

0. $(9 \times 9 \times 9) \times (7 \times 7 \times 7)$