Question

find the value of the expression.
(2/3)^7 multiplied by 1.5^7

Answer 1

To find the value of the expression \((\frac{2}{3})^7 \times (1.5)^7\), we can simplify this using the property of exponents:

\[
a^m \times b^m = (a \times b)^m
\]

In our case, we can rewrite the expression as:

\[
(\frac{2}{3} \times 1.5)^7
\]

Now, let's compute \(\frac{2}{3} \times 1.5\):

\[
1.5 = \frac{3}{2}
\]

So,

\[
\frac{2}{3} \times 1.5 = \frac{2}{3} \times \frac{3}{2} = 1
\]

Thus,

\[
(\frac{2}{3} \times 1.5)^7 = 1^7 = 1
\]

Therefore, the value of the expression \((\frac{2}{3})^7 \times (1.5)^7\) is

\[
\boxed{1}
\]