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kodGreya [7K]
3 years ago
9

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 tim

es 6 times 6 / 6 times 6 times 6 c: 6^4/6^2 d: 6^5 times 6^7/6^10
Mathematics
2 answers:
bearhunter [10]3 years ago
4 0

Answer:

acd

Step-by-step explanation:

Kamila [148]3 years ago
3 0

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

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

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

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