Question

Usando as propriedades da potência, calcule o valor de:

Answer 1

quando multiplica com base igual soma os espoentes e com base diferente conserva o espoente e multiplica os espoentes quando divide é ao contrario se é base igual subtrai os espoentes e de base duferebte e espoente igual divide a base.

Answer 2

a)
$\displaystyle \frac{2^4\cdot2^{10}\cdot2^{3}}{2^{3}\cdot2^{6}}=\frac{2^{(4+10+3)}}{2^{(3+6)}}=\frac{2^{17}}{2^9}=2^{(17-9)}=2^{8}=\boxed{256}$

b)
$\displaystyle [7^{5}:7^{3}]\cdot7^2=\left[\frac{7^5}{7^3}\right]\cdot7^2=[7^{(5-3)}]\cdot7^2=7^2\cdot7^2=7^{(2+2)}=7^4=\boxed{2401}$

c)
$\displaystyle (7\cdot4)^2=7^2\cdot4^2=49\cdot16=\boxed{784}$

d)
$\displaystyle \left[\left(-\frac{1}{2}\right)^3\right]^2=\left[-\frac{1^3}{2^3}\right]^2=\left[-\frac{1}{8}\right]^2=-\frac{1^2}{8^2}=\frac{1}{64}=\boxed{64^{-1}}$

e)
$\displaystyle \left(\frac{1}{4}\right)^{-3}=\left(\frac{1^{-1}}{4^{-1}}\right)^3=\left(\frac{4}{1}\right)^3=(4)^3=4^3=\boxed{64}$

d)
$\displaystyle \left[\left(-\frac{1}{3}\right)^{-6}\right]^{-1}=\left[\left(-\frac{1^{-1}}{3^{-1}}\right)^6\right]^{-1}=\left[\left(-3\right)^6\right]^{-1}=\left[729\right]^{-1}=\boxed{\frac{1}{729}}$