Question

Select all the expressions that equal 6-1 D 6-5.62 () -16% D 6.63

Answer 1

The given expression is;

$6^{-10}$

A)

$6^{-5}\cdot6^2_{}$

Since bases of both the terms are same i.e., 6

So, when multiplying two powers that have the same base, you can add the exponents.

$\begin{gathered} 6^{-5}\cdot6^2_{}=6^{-5+2} \\ 6^{-5}\cdot6^2_{}=6^{-3} \\ \text{Since, 6}^{-3}\ne6^{-10} \end{gathered}$

So, Option A is not the right answer;

B)

$(\frac{1}{6^2})^5$

Apply the power rule of exponents;

$\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5^{} \\ (\frac{1}{6^2})^5=6^{-10} \\ \text{ Since, the given expression is 6}^{-10} \\ So,6^{-10}=6^{-10} \end{gathered}$

Thus, Option B is the right answer

C)

$(6^{-5})^2$

Apply the exponents rule;

$\begin{gathered} (6^{-5})^2=6^{-10} \\ \text{ Since, the given expression is; 6}^{-10} \\ 6^{-10}=6^{-10} \end{gathered}$

Therefore, Option C is the right answer

D)

$\frac{6^5\cdot6^{-3}}{6^{-8}}$

Simplify the expression;

since the bases are same so the in the multiplication the exponent value will be add up and during division, the exponent value will be subtract;

$\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^2}{6^{-8}} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{2-(-8)} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{2+8} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{10} \\ \text{ Since, the given expression is 6}^{-10} \\ and6^{-10}\ne6^{10} \end{gathered}$

Therefore, Option D is not the right answer

E)

$\frac{6^{-3}}{6^7}$

Simplify the expression by using division rule of exponent;

To divide exponents (or powers) with the same base, subtract the exponents:

$\begin{gathered} \frac{6^{-3}}{6^7}=6^{-3-7} \\ \frac{6^{-3}}{6^7}=6^{-10} \\ \text{ Since, the given expression is 6}^{-10} \\ 6^{-10}=6^{-10} \end{gathered}$

So, option E is the correct answer

Answer : B, C,