Question

Select the three expressions that are equivalent to 6^{2}6 2 6, squared. a: (6^9/6^8)^2 b: 6 times 6 times 6 times 6 times 6 times 6 times 6 / 6 times 6 times 6 c: 6^4/6^2 d: 6^5 times 6^7/6^10

Answer 1

Question:

Select the three expressions that are equivalent to $6^2$:

a: $(\frac{6^9}{6^8})^2$

b: $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$

c: $\frac{6^4}{6^2}$

d: $\frac{6^5 * 6^7}{6^{10}}$

Answer:

a: $(\frac{6^9}{6^8})^2$

c: $\frac{6^4}{6^2}$

d: $\frac{6^5 * 6^7}{6^{10}}$

Step-by-step explanation:

Given

$6^2$:

Required

Find equivalent expressions

To solve this question; we'll simplify options a to do, one after the other

a: $(\frac{6^9}{6^8})^2$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that;

$(\frac{6^9}{6^8})^2 = (6^{9-8})^2$

$(\frac{6^9}{6^8})^2 = (6^{1})^2$

From laws of indices;

${a^m}^n = a^{m*n} = a^{mn}$

This implies that

$(\frac{6^9}{6^8})^2 = (6^{1*2})$

$(\frac{6^9}{6^8})^2 = 6^{2}$

Hence,  $(\frac{6^9}{6^8})^2$ is equivalent to $6^2$

b. $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$

From laws of indices;

$a^m * a^n = a^{m+n}$

This implies that

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{1+1+1+1+1+1}}{6^{1+1+1}}$

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{6}}{6^{3}}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{6-3}$

$\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{3}$

Hence; $\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }$ is not equivalent to $6^2$

c.  $\frac{6^4}{6^2}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6^4}{6^2} = 6^{4-2}$

$\frac{6^4}{6^2} = 6^{2}$

Hence, $\frac{6^4}{6^2}$ is equivalent to $6^2$

d.  $\frac{6^5 * 6^7}{6^{10}}$

From laws of indices;

$a^m * a^n = a^{m+n}$

This implies that

$\frac{6^5 * 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}}$

From laws of indices;

$\frac{a^m}{a^n} = a^{m-n}$

This implies that

$\frac{6^5 * 6^7}{6^{10}} = 6^{5+7-10}$

$\frac{6^5 * 6^7}{6^{10}} = 6^{2}$

Hence, $\frac{6^5 * 6^7}{6^{10}}$ is equivalent to $6^2$

Answer 2

Answer:

6^2

Step-by-step explanation:

Just Like That Guy Said