Question

Study the box below. Follow the directions and write the answer in the space provided.

Answer 1

The expressions in their expanded forms are:

• $7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7$.
• $4^5 = 4 \times 4 \times 4 \times 4 \times 4$.
• $x^3 = x \times x \times x$.
• $a^2 \cdot b^2 = a \times a \times b \times b$.
• $8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9$.
• $2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3$.

Exponents

The exponent of a number or an expression is used to expand the expression.

Take for instance, the following expression in its exponential form

$3^2$

The above expression means that, the value of 3 multiplied twice

The problems

The first expression is given as 7^8.

This represents the value of 7 multiplied by itself 8 times.

So, we have:

$7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7$

Using the above as a guide, the expanded forms of the other expressions are:

• $4^5 = 4 \times 4 \times 4 \times 4 \times 4$.
• $x^3 = x \times x \times x$.
• $a^2 \cdot b^2 = a \times a \times b \times b$.
• $8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9$.
• $2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3$.

Read more about expansions at:

brainly.com/question/4344214