Question

(1 7/9)^6× 6^13/8^10

Answer 1

(1 7/9)^6* 6^13/8^10
(7/9)^6 * 2^13*3^13 / (2^3)^10
7^6/9^6*2^13*3^13 /2^30
7^6/3^12*3^13/2^17
7^6*3/2^17
3*7^6/2^17

Answer 2

Let's break it down step by step:

$\left( \frac{1}{\frac{7}{9}} \right)^6 \times \frac{6^{13}}{8^{10}}$

First, simplify the fraction in the parentheses:

$\left( \frac{1}{\frac{7}{9}} \right)^6$

To simplify a fraction in the denominator, you can multiply the numerator and denominator by the reciprocal of the fraction:

$\frac{1}{\frac{7}{9}} = 1 \times \frac{9}{7} = \frac{9}{7}$

So, the expression becomes:

$\left( \frac{9}{7} \right)^6 \times \frac{6^{13}}{8^{10}}$

Now, let's simplify the powers:

$\left( \frac{9}{7} \right)^6 = \frac{9^6}{7^6}$

$\frac{6^{13}}{8^{10}} = \frac{2^{13 \times 3}}{2^{10 \times 3}} = \frac{2^{39}}{2^{30}} = 2^{39-30} = 2^9$

Now, substitute these back into the expression:

$\frac{9^6}{7^6} \times 2^9$

You can leave it like this or calculate the numerical value if needed.