a) \(\left(\frac{3}{5}\right)^{15}:\left(\frac{9}{25}\right)^5=\left(\frac{3}{5}\right)^{15}:\left(\left(\frac{3}{5}\right)^2\right)^5=\left(\frac{3}{5}\right)^{15}:\left(\frac{3}{5}\right)^{10}=\left(\frac{3}{5}\right)^5\)

b) \(5-\left(-\frac{5}{11}\right)^0+\left(\frac{1}{3}\right)^2:3=5-1+\frac{1}{9}:3=4+\frac{1}{27}=4\frac{1}{27}\)

c) \(2^3+3.\left(\frac{1}{2}\right)^0+\left(-2\right)^2:\frac{1}{2}.8=8+3.1+4:\frac{1}{2}.8=8+3+64=75\)

d) \(\left(-1\right)^{-1}-\left(-\frac{3}{5}\right)^0+\left(\frac{1}{2}\right)^{2:2}=-1-1+\left(\frac{1}{2}\right)^1=-2+\frac{1}{2}=-\frac{3}{2}\)

bạn giải thích cho mình phần a nhé

a) \(25^3:5=5^{6-1}=5^4=625\)

Học tốt~

1) Tính

a) 25³ : 5² = (5²)³ : 5² = 5⁶ : 5² = 5⁴ = 625

\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 3² . \(\dfrac{1}{81}\) . 3² = 3² . 3² . \(\dfrac{1}{3^4}\) . 3² = 9

2) Tìm x thuộc Q, biết:

a) 3^{x + 2} = 27

=> 3^{x + 2} = 3³

x + 2 = 3

x = 3 - 2

x = 1

b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)

\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)

\(\dfrac{1}{2}x-3=3^{ }\)

\(\dfrac{1}{2}x=3+3\)

\(\dfrac{1}{2}x=9\)

\(x=9:\dfrac{1}{2}\)

\(x=18\)

c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)

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

\(x-\dfrac{1}{2}=-3\)

\(x=-3+\dfrac{1}{2}\)

\(x=\dfrac{-5}{2}\)

d) 5 . 5^{x + 1} = 125

5^{x + 1} = 125 : 5

5^{x + 1} = 25

5^{x + 1} = 5²

x + 1 = 2

x = 2 - 1

x = 1.

a) 4. ( 1.1/4)² + [(3/4)² : (5/4)³] : (3/2)³

= 4.1/16 + [9/16 : 125/64] : 27/8

= \(\frac{1}{4}+\frac{9}{16}:\frac{125}{64}:\frac{27}{8}=\frac{1}{4}+\frac{36}{125}:\frac{27}{8}\)

= \(\frac{1}{4}+\frac{36}{125}.\frac{8}{27}\)

=\(\frac{1}{4}+\frac{32}{375}=\frac{375}{1500}+\frac{128}{1500}=\frac{503}{1500}\)

b] = 2^3 + 3 x 1 - 1 + ( 2^2 x 2 ) x 2^3

= 2^3 + 3 - 1 + 2^3 x 2^3

= 2^3 + 2 + 2^6 = 74

a] = 4 x ( 1/4 )²  + ( 3²/4² : 5³/4³ ) : 27/8

= 4 x 1/16 + ( 3² x 4/5³ ) x 8/27

= 1/4 + 36/5³ x 8/27 = 1/4 + 4/125 x 8/3 = 503/1500 sấp sỉ 0,335333

a)\(\left(\frac{1}{5}\right)^{3x-1}=\frac{1}{25}\)

\(\Leftrightarrow\left(\frac{1}{5}\right)^{3x-1}=\left(\frac{1}{5}\right)^2\)

<=> 3x-1=2

<=> 3x=3

<=> x=1

c) \(\left(\frac{2}{3}\right)^{1-x}=\left(\frac{2}{3}\right)^3\)

<=> 1-x=3

<=>x=-2

d) (0,7)^3x+1=(0,7)³

<=> 3x+1=3

<=> 3x=2

<=> x=2/3

b) \(\left(\frac{4}{7}\right)^{x+2}=\frac{7}{4}\)

\(\Leftrightarrow\left(\frac{4}{7}\right)^{x+2}=\left(\frac{4}{7}\right)^{-1}\)

<=> x+2=-1

<=> x=-3

k) \(\left(\frac{1}{9}\right)^{25}:\left(\frac{1}{3}\right)^{30}\)

\(=\left[\left(\frac{1}{3}\right)^2\right]^{25}:\left(\frac{1}{3}\right)^{30}\)

\(=\left(\frac{1}{3}\right)^{50}:\left(\frac{1}{3}\right)^{30}\)

\(=\left(\frac{1}{3}\right)^{50-30}\)

\(=\left(\frac{1}{3}\right)^{20}\)

h) \(\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{4}\right)^{20}\)

\(=\left(\frac{1}{2}\right)^{15}.\left[\left(\frac{1}{2}\right)^2\right]^{20}\)

\(=\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{2}\right)^{40}\)

\(=\left(\frac{1}{2}\right)^{15+40}\)

\(=\left(\frac{1}{2}\right)^{55}\)

(√25+√49) x 14 - |-3|

= (5+7)x14-3

=12x14-3

=168-3

=165

2³ + 3 x (2017)⁰ + (-2)² : 1/2

=8+3x1+4:1/2

=8+3+8

=11+8

=19