Exercise$\left(\frac{2}{9}m^x-\frac{3}{7}n^{x+1}\right)^2$
Step-by-step Solution
Intermediate steps
1
Expand $\left(\frac{2}{9}m^x-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
$\left(\frac{2}{9}m^x\right)^2+\frac{4}{9}\cdot -\frac{3}{7}m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
Explain this step further
2
The power of a product is equal to the product of it's factors raised to the same power
$\left(\frac{2}{9}\right)^2\left(m^x\right)^2+\frac{4}{9}\cdot \left(-\frac{3}{7}\right)m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
3
Calculate the power $\left(\frac{2}{9}\right)^2$
$\frac{4}{81}\left(m^x\right)^2+\frac{4}{9}\cdot -\frac{3}{7}m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
4
Simplify $\left(m^x\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x$ and $n$ equals $2$
$\frac{4}{81}m^{2x}+\frac{4}{9}\cdot \left(-\frac{3}{7}\right)m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
5
Multiplying fractions $\frac{4}{9} \times -\frac{3}{7}$
$\frac{4}{81}m^{2x}-\frac{4}{21}m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$
Final answer to the exercise $\frac{4}{81}m^{2x}-\frac{4}{21}m^xn^{\left(x+1\right)}+\left(-\frac{3}{7}n^{\left(x+1\right)}\right)^2$