Question

plase solve this!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Concept:

The rules of exponentiation:

Product  $x^ax^b=x^{a+b$

Quotient        $x^a \div x^b=x^{a-b}$

Power of power $(x^a)^b=x^{ab$

Power of a product $(xy)^a=x^ay^a$

Step-by-step explanation:

(a) $6^2 \times 6^x=6^6$

► 2+x = 6

► x = 4

(b) $9 \times 3^{x+2} = 729$

► $3^2\times 3^{x+2 } = 3^ 6$

► 2+x+2 = 6

► x= 6-4

►x= 2

(c) $\frac{2}{43^3}\times 2^2= x^3$

►$2\times 2^2 = x^3\times43^3$

►$2^3 = (x\times43)^3$

► 2 = x×43

► x = 2/43

(d)$(\frac{5}{3}) ^5\times(\frac{5}{3}) ^{11} = (\frac{5}{3}) ^{8x}$

► 5+11 = 8x

► 8x = 16

► x =2

(e) $(\frac{3}{8}) ^2\times(\frac{3}{8}) ^{8} = (\frac{3}{8}) ^{6x-2}$

► 2+8 = 6x -2

► 6x = 12

► x = 2

(f) $(\frac{125}{8}) ^5\times(\frac{125}{8}) ^{x} = (\frac{5}{2}) ^{18}$

►$(\frac{5}{2}) ^3^\times^5\times(\frac{5}{2}) ^{3\times x} = (\frac{5}{2}) ^{18}$

► 3× 5 + 3× x = 18

► 15 +3x = 18

►3x = 18-15

► 3x = 3

► x =1

Final Answer:

(a) 4

(b) 2

(c) 2/43

(d) 2

(e) 2

(f) 1

Answer 2

Concept:

The rules of exponentiation:

Product x^ax^b=x^{a+b

Quotient x^a \div x^b=x^{a-b}x

a

÷x

b

=x

a−b

Power of power (x^a)^b=x^{ab

Power of a product (xy)^a=x^ay^a(xy)

a

=x

a

y

a

Step-by-step explanation:

(a) 6^2 \times 6^x=6^66

2

×6

x

=6

6

► 2+x = 6

► x = 4

(b) 9 \times 3^{x+2} = 7299×3

x+2

=729

► 3^2\times 3^{x+2 } = 3^ 63

2

×3

x+2

=3

6

► 2+x+2 = 6

► x= 6-4

►x= 2

(c) \frac{2}{43^3}\times 2^2= x^3

43

3

2

×2

2

=x

3

►2\times 2^2 = x^3\times43^32×2

2

=x

3

×43

3

►2^3 = (x\times43)^32

3

=(x×43)

3

► 2 = x×43

► x = 2/43

(d)(\frac{5}{3}) ^5\times(\frac{5}{3}) ^{11} = (\frac{5}{3}) ^{8x}(

3

5

)

5

×(

3

5

)

11

=(

3

5

)

8x

► 5+11 = 8x

► 8x = 16

► x =2

(e) (\frac{3}{8}) ^2\times(\frac{3}{8}) ^{8} = (\frac{3}{8}) ^{6x-2}(

8

3

)

2

×(

8

3

)

8

=(

8

3

)

6x−2

► 2+8 = 6x -2

► 6x = 12

► x = 2

(f) (\frac{125}{8}) ^5\times(\frac{125}{8}) ^{x} = (\frac{5}{2}) ^{18}(

8

125

)

5

×(

8

125

)

x

=(

2

5

)

18

►$$(\frac{5}{2}) ^3^\times^5\times(\frac{5}{2}) ^{3\times x} = (\frac{5}{2}) ^{18}$$

► 3× 5 + 3× x = 18

► 15 +3x = 18

►3x = 18-15

► 3x = 3

► x =1

Final Answer:

(a) 4

(b) 2

(c) 2/43

(d) 2

(e) 2

(f) 1