Question

Tính :a) \(^{25^3}\)\(\div\) \(^{5^2}\)

​b)\(\left(\frac{3}{7}\right)^{21}\div\left(\frac{9}{49}\right)^6\)   

c) 3\(-\)\(\left(\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2\div2\)

d) \(\left(\frac{-7}{4}\div\frac{5}{8}\right)\times\frac{11}{16}\)

e) \(\frac{2}{3}+\frac{1}{3}\times\frac{-6}{10}\)

 

Answer 1

a. \(25^3:5^2\)
\(=\left(5^2\right)^3:5^2\)
\(=5^6:5^2=5^4\)
b. \(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6\)
\(=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6\)
\(=\left(\frac{3}{7}\right)^{21-\left(2+6\right)}=\left(\frac{3}{7}\right)^{21-12}=\left(\frac{3}{7}\right)^9\)

Answer 2

\(a,25^3:5^2\)

=\(\left(5^2\right)^3:5^2\)

=\(5^6:5^2\)

=\(5^4\)

\(b,\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6\)

=\(\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6\)

\(=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}\)

\(=\left(\frac{3}{7}\right)^9\)

\(c,3-\left(\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2\)

=\(3-1+\frac{1}{4}:2\)

\(=2+\frac{1}{4}\cdot\frac{1}{2}\)

\(=2+\frac{1}{8}\)

\(=\frac{17}{8}\)

\(d,\left(-\frac{7}{4}:\frac{5}{8}\right)\cdot\frac{11}{16}\)

\(=\left(-\frac{7}{4}\cdot\frac{8}{5}\right)\cdot\frac{11}{16}\)

\(=-\frac{14}{5}\cdot\frac{11}{16}\)

\(=-\frac{77}{40}\)

\(e,\frac{2}{3}+\frac{1}{3}\cdot\frac{-6}{10}\)

\(=\frac{2}{3}-\frac{1}{5}\)

\(=\frac{7}{15}\)

Answer 3

c. \(3-\left(\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2\)
\(=3+1+\frac{1}{4}.\frac{1}{2}\)
\(=4+\frac{1}{8}\)
\(=\frac{33}{8}\)