use the laws of exponents to simplify the expression. \n\\begin{bmatrix}7^{\\frac{12}{5}}\\end{bmatrix}\\begi…

use the laws of exponents to simplify the expression. \n\\begin{bmatrix}7^{\\frac{12}{5}}\\end{bmatrix}\\begin{bmatrix}7^{-\\frac{2}{5}}\\end{bmatrix}\\begin{bmatrix}7^{\\frac{12}{5}}\\end{bmatrix}\\begin{bmatrix}7^{-\\frac{2}{5}}\\end{bmatrix}=\\square \n(type an integer or a simplified fraction.)

use the laws of exponents to simplify the expression. \n\\begin{bmatrix}7^{\\frac{12}{5}}\\end{bmatrix}\\begin{bmatrix}7^{-\\frac{2}{5}}\\end{bmatrix}\\begin{bmatrix}7^{\\frac{12}{5}}\\end{bmatrix}\\begin{bmatrix}7^{-\\frac{2}{5}}\\end{bmatrix}=\\square \n(type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Aplicar la ley de exponentes ( a^m \cdot a^n = a^{m + n} )

Tenemos la expresión ( \left(7^{\frac{12}{5}}\right)\left(7^{-\frac{2}{5}}\right) ). Usando la ley de exponentes para la multiplicación de potencias con la misma base, sumamos los exponentes: ( 7^{\frac{12}{5} + \left(-\frac{2}{5}\right)} )

Step2: Sumar los exponentes

Calculamos la suma de los exponentes: ( \frac{12}{5} - \frac{2}{5} = \frac{12 - 2}{5} = \frac{10}{5} = 2 )

Step3: Simplificar la potencia

Entonces, ( 7^2 = 49 )

Answer:

49