Question

Select the equivalent expression.

Answer 1

Answer:

$\frac{7^{15}}{3^{30}}$

Step-by-step explanation:

The given expression is:

$(\frac{3^{-6}}{7^{-3}})^{5}$

Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:

$(\frac{3^{-6}}{7^{-3}})^{5}\\\\ = (\frac{7^{3}}{3^{6}} )^{5}$

The exponent 5 can be distributed to both numerator and denominator as shown:

$(\frac{7^{3}}{3^{6}} )^{5}\\\\ = \frac{(7^{3})^{5}}{(3^{6})^{5}}$

The power of a power can be written as a product. i.e.

$\frac{(7^{3})^{5}}{(3^{6})^{5}}\\\\ =\frac{7^{15}}{3^{30}}$

So, the expression similar to the given expression and with positive exponents is: $\frac{7^{15}}{3^{30}}$

Answer 2

Answer:

frac{7^{15}}{3^{30}}

Step-by-step explanation: