Question

se the power of a power property to determine if the following expressions are equal.
$8^{\frac{4}{5}}$ and $16^{\frac{3}{5}}$

ne expressions $\boldsymbol{\bigtriangledown}$ equal. the expression $8^{\frac{4}{5}}$ can be rewritten as $\left(2^{\boldsymbol{\square}}\
ight)^{\frac{4}{5}}$ and then as $2^{\boldsymbol{\square}}$, and $16^{\frac{3}{5}}$ can be rewritten as $\left(2^{\boldsymbol{\square}}\
ight)^{\frac{3}{5}}$ and then as $2^{\boldsymbol{\square}}$. the
expressions have the same base, $\boldsymbol{\bigtriangledown}$ equal.
type integers or simplified fractions.)

Explanation:

Step1: Rewrite the bases as powers of 2

Since \(8 = 2^3\) and \(16=2^4\).
So, \(8^{\frac{4}{5}}=(2^3)^{\frac{4}{5}}\) and \(16^{\frac{3}{5}}=(2^4)^{\frac{3}{5}}\).

Step2: Apply the Power - of - a - Power Property \((a^m)^n=a^{mn}\)

For \((2^3)^{\frac{4}{5}}\), using the property \((a^m)^n=a^{mn}\), we get \(2^{3\times\frac{4}{5}}=2^{\frac{12}{5}}\).
For \((2^4)^{\frac{3}{5}}\), using the property \((a^m)^n=a^{mn}\), we get \(2^{4\times\frac{3}{5}}=2^{\frac{12}{5}}\).

Answer:

The first drop - down: are. The second box: \(3\). The third box: \(\frac{12}{5}\). The fourth box: \(4\). The fifth box: \(\frac{12}{5}\). The second drop - down: their exponents are.