Question

do you know how?

1. write an equivalent expression for (7^{12}div7^{4}).
2. write an equivalent expression for ((8^{4})^{4}).
3. a billboard has the given dimensions.

using exponents, write two equivalent expressions for the area of the rectangle.

1. write an equivalent expression for (18^{9}div18^{1}).

Explanation:

Question 5

Step1: Recall the exponent rule for division ($\frac{a^m}{a^n}=a^{m - n}$)

Given the expression $7^{12}\div7^{4}$, here $a = 7$, $m = 12$, $n = 4$.

Step2: Apply the exponent division rule

Using the rule $\frac{a^m}{a^n}=a^{m - n}$, we substitute the values: $7^{12-4}=7^{8}$

Step1: Recall the exponent rule for power of a power ($(a^m)^n=a^{m\times n}$)

Given the expression $(8^{4})^{4}$, here $a = 8$, $m = 4$, $n = 4$.

Step2: Apply the power of a power rule

Using the rule $(a^m)^n=a^{m\times n}$, we calculate $4\times4 = 16$, so the expression becomes $8^{16}$

Step1: Recall the formula for the area of a rectangle ($A=l\times w$)

The area of a rectangle is given by the product of its length and width. So $A = 7^{2}\times4^{2}$

Step2: Simplify the expression (optional, but to show equivalence)

We can also use the property $(ab)^n=a^n\times b^n$. So $7^{2}\times4^{2}=(7\times4)^{2}=28^{2}$

Second equivalent expression:

We can calculate the numerical values first. $7^{2}=49$ and $4^{2} = 16$, then the area is $49\times16=784$. Also, $28^{2}=784$ and $7^{2}\times4^{2}=49\times16 = 784$. But as per the requirement of using exponents, two equivalent expressions using exponents are:

Answer:

$7^{8}$

Question 6