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Sliva [168]
4 years ago
10

Simplify the following expression.A.49B.1/14C.1/49D.14

Mathematics
2 answers:
Anna35 [415]4 years ago
5 0

Answer:

C

Step-by-step explanation:

Using the rules of exponents

• a^{m} × a^{n} ⇔ a^{(m+n)}

• a^{-m} ⇔ \frac{1}{a^{m} }

Hence

7^{-5/6-7/6} = 7^{-\frac{12}{6} } = 7^{-2}, then

7^{-2} = \frac{1}{7^{2} } = \frac{1}{49} → C

spayn [35]4 years ago
5 0

ANSWER

C. 1/49

EXPLANATION

The given expression is

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }

Recall that:

{a}^{m}  \times  {a}^{n}  =  {a}^{m + n}

We apply this product rule of exponents to get:

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }  =  {7}^{ -  \frac{5}{6} +  -  \frac{7}{6}  }

This implies that:

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }  =  {7}^{ -  \frac{12}{6} }

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }  =  {7}^{ - 2}

Recall again that:

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

We apply this rule to get:

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }  =   \frac{1}{ {7}^{2} }

This simplifies to:

{7}^{ -  \frac{5}{6} }  \times {7}^{ -  \frac{7}{6} }  =   \frac{1}{49}

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