Question

decide whether each equation is true or false. select the correct choice in each row.
a. $4^3 = 4 + 4 + 4$ \\(\bigcirc\\) true \\(\bigcirc\\) false
b. $\frac{1}{4} \cdot \frac{1}{4} = \left(\frac{1}{4}\
ight)^2$ \\(\bigcirc\\) true \\(\bigcirc\\) false
c. $x \cdot x \cdot x \cdot x \cdot x = 5x$ \\(\bigcirc\\) true \\(\bigcirc\\) false
d. $3^2 = 2 \cdot 2 \cdot 2$ \\(\bigcirc\\) true \\(\bigcirc\\) false
e. $9^2 = 3^4$ \\(\bigcirc\\) true \\(\bigcirc\\) false
f. $\frac{1}{b} \cdot \frac{1}{b} \cdot \frac{1}{b} \cdot \frac{1}{b} = \left(\frac{1}{b}\
ight)^4$ \\(\bigcirc\\) true \\(\bigcirc\\) false

Explanation:

Part a

Step1: Recall exponent definition

$a^n$ means $n$ times multiplication of $a$, so $4^3 = 4\times4\times4$, while $4 + 4+ 4=12$ and $4\times4\times4 = 64$, so they are not equal.

Step1: Recall exponent property

By the definition of exponent, $(\frac{1}{4})^2=\frac{1}{4}\times\frac{1}{4}$, so the left - hand side and the right - hand side are equal.

Step1: Recall exponent definition

$x\cdot x\cdot x\cdot x\cdot x=x^5$ (since there are 5 $x$'s multiplied together), and $5x$ means $x + x+x+x+x$. These two expressions are not the same (unless $x = 0$ or $x = 5$, but in general, they are different).

Answer:

False

Part b