Question

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

Answer 1

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

Answer 2

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:

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