Question

Tính

a) \(\left(-52\right)^3:13^3\)

b) \(\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{4}\right)^6\)

c) \(\left(\dfrac{1}{9}\right)^{30}:\left(\dfrac{1}{3}\right)^{56}\)

d) \(\left(\dfrac{1}{8}\right)^5:\left(\dfrac{1}{16}\right)^3\)

Answer 1

a/ \(\left(-52\right)^3:13^3=\left(-52:13\right)^3=\left(-4\right)^3\)

b/ \(\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{4}\right)^6=\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{2}\right)^{12}=\left(\dfrac{1}{2}\right)^3\)

c/ \(\left(\dfrac{1}{9}\right)^{30}:\left(\dfrac{1}{3}\right)^{56}=\left(\dfrac{1}{3}\right)^{60}:\left(\dfrac{1}{3}\right)^{56}=\left(\dfrac{1}{3}\right)^4\)

d/ \(\left(\dfrac{1}{8}\right)^5:\left(\dfrac{1}{16}\right)^3=\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{2}\right)^{12}=\left(\dfrac{1}{2}\right)^3\)

Answer 2

Tính

a) (- 52)³ : 13³ = (- 52 : 13)³ = (- 4)³ = - 64

b) \(\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{4}\right)^6\)

\(=\left(\dfrac{1}{2}\right)^{15}:\left[\left(\dfrac{1}{2}\right)^2\right]^6\)

\(=\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{2}\right)^{12}\)

\(=\left(\dfrac{1}{2}\right)^3\)

\(=\dfrac{1}{8}\)

c) \(\left(\dfrac{1}{9}\right)^{30}:\left(\dfrac{1}{3}\right)^{56}\)

\(=\left[\left(\dfrac{1}{3}\right)^2\right]^{30}:\left(\dfrac{1}{3}\right)^{56}\)

\(=\left(\dfrac{1}{3}\right)^{60}:\left(\dfrac{1}{3}\right)^{56}\)

\(=\left(\dfrac{1}{3}\right)^4\)

\(=\dfrac{1}{81}\)

d) \(\left(\dfrac{1}{8}\right)^5:\left(\dfrac{1}{16}\right)^3\)

\(=\left[\left(\dfrac{1}{2}\right)^3\right]^5:\left[\left(\dfrac{1}{2}\right)^4\right]^3\)

\(=\left(\dfrac{1}{2}\right)^{15}:\left(\dfrac{1}{2}\right)^{12}\)

\(=\left(\dfrac{1}{2}\right)^3\)

\(=\dfrac{1}{8}.\)