Question

find the value of the expression.
(5/7)^10 multiplied by 1.4^9

Answer 1

To evaluate the expression \((\frac{5}{7})^{10} \times 1.4^9\), we first rewrite \(1.4\) as a fraction:

\[
1.4 = \frac{14}{10} = \frac{7}{5}
\]

Now, we can substitute this into our expression:

\[
1.4^9 = \left(\frac{7}{5}\right)^9
\]

Now we can rewrite the entire expression:

\[
\left(\frac{5}{7}\right)^{10} \times \left(\frac{7}{5}\right)^9
\]

Using the properties of exponents, this simplifies as follows:

\[
\left(\frac{5}{7}\right)^{10} \times \left(\frac{7}{5}\right)^{9} = \frac{5^{10}}{7^{10}} \times \frac{7^9}{5^9}
\]

We can combine the fractions:

\[
= \frac{5^{10} \times 7^9}{7^{10} \times 5^9}
\]

This simplifies to:

\[
= \frac{5^{10 - 9}}{7^{10 - 9}} = \frac{5^1}{7^1} = \frac{5}{7}
\]

Thus, the value of the expression \((\frac{5}{7})^{10} \times 1.4^9\) is

\[
\boxed{\frac{5}{7}}
\]