Just Indices

$\frac{{48}^{8}}{{4}^{8}}={12}^{8}$

$\frac{{48}^{8}}{{12}^{8}}={4}^{8}$

${4}^{8}={16}^{a}$

${4}^{8}={16}^{4}$

$a=4$

Using laws of exponent, $a^{m} \times a^{n} = a^{m+n}$

$48^{8} = 12^{8} \times 4^{8}$

$48^{8} = 12^{8} \times 4^{2} \times 4^{2} \times 4^{2} \times 4^{2}$

$48^{8} = 12^{8} \times 16 \times 16 \times 16 \times 16$

$48^{8} = 12^{8} \times 16^{4}$

Therefore, $a$ = 4

48^8 = 12^8 X 16^a

Or, 12^8 X 16^a = 48^8

Or, 16^a = 48^8/12^8

Or, 16^a = 4^8

Or, 2^4.a = 2^2.8

Or, 2^4a = 2^16

Or, 4a = 16

Or, a = 16/4

And Finally, a = 4

488= 128*16a i.e 16a=(48^8)/(12^8) or, log16a=log65536 or, a= (log65536)/(log16) i.e a=4

(6^8)(8^8)=(6^8)(2^8) * 16^a

(6^8)(8^8)/(6^8)(2^8) =16^a (8^8)/(2^8)= 16^a

(2^8)(4^8)/(2^8)=16^a

(4^8)=16^a

(4^8)=(4^a)(4^a) a=4

48^8 =12^8 x 16^a

48^8/12^8 = 16^a

(48/12)^8 = 16^a

4^8 = 16^a (make bases the same. 4^2 = 16)

4^(2x4) = 16^a

(4^2)^4 = 16^a

16^4 = 16^a

4 = a (yay!)

Good question........................

48^8=12^8*16^a

8log48=8log12+a log16

8log(12*4)=8log12+a log(2^4)

8log12+ 8log 4 = 8 log 12 + 4a log 2

8 log 12 cancels out So, 8 log (2^2) = 4a log2 16 log 2 = 4a log 2

Therefore, a= 16/4=4

8log48 = 8log12 + alog16 (8log48-8log12)/log16 = a = 4

Remembering some properties of potency:

1 -

(a * b) ^n = (a^n) * (b^n)

2 -

a^b^n = a^b*n

Where a, b and n are positive integers

We can use the same reasoning:

(48 ^8)= (12 * 4)^8 = 12^8*4^8

16^a = 4^2^a = 4^2*a

Thus,

48^8 = 12^8 * 16^a

12^8 * 4^8 = 12^8 * 16^a

4^8 = 4^2*a

As the potencies are from same base, so:

8 = 2*a

a = 4

(48 to the power 8)=(12 to the power 8)×(16 to the power a)

(48 to the power 8)÷(12 to the power 8)=(16 to the power a)

(4 to the power 8)=(16 to the power a); (4 to the power 8)=(4 to the power 2a) 2a=8; a=8÷2; a=4.

$48^{8} = 12^{8} \times 16^{a}$

$3^{8} \times 16^{8} = 3^{8} \times 4^{8} \times 16^{a}$

$16^{8} = 4^{8} \times 16^{a}$

$4^{16} = 4^{8} \times 4^{2a}$

$16 = 8 + 2a$

$8 = 2a$

$a = \boxed{4}$

48^8 can b written as 12^8 4^8 n So 12^8 4^8=16^a*12^8 Cancel 12^8 on both sides. 4^8=4^2a 8=2a A=4

(48)^8=(12x4)^8 =12^8x4^8=12^8x16^4

a= 4

(12X4)^8 = 12^8 X 4^8

4^(2x4) = 16^4

Given:

$48^{8}=12^{8} \times 16^{a}$

Divide both sides by $12^{8}$ .

$\frac{48^{8}}{12^{8}}=\frac{12^{8} \times 16^{a}}{12^{8}}$

Simplify.

$\frac{48^{8}}{12^{8}}=16^{a}$

Since $12$ is a factor of $48$ , write $48$ as a $12\cdot4$ in order to make it cancel with the denominator.

$\frac{(12\cdot4)^{8}}{12^{8}}=16^{a}\\\frac{12^{8}\cdot4^{8}}{12^{8}}=16^{a}\\4^{8}=16^{a}$

$16$ can be written as $4^{2}$ . Write it as a power of $4$ so the exponents can be equated.

$4^{8}=(4^{2})^{a}\\4^{8}=4^{2a}\\8=2a\\\boxed{a=4}$

48^8 = 12^8 * 16^a 48^8/12^8 = 16^a ( 48/12)^8 = 16^a 4^8 = 16^a 16^a =65536 65536 = 16^4 So, a = 4

48^8 = 12^8 x (48/12)^8

48/12 = 4

4^8 = 16^(8/2) = 16^4

$48 ^{ 8 }={ 12 }^{ 8 }\times { 16 }^{ a }\\ \\ { 48 }^{ 8 }={ { (2 }^{ 4 }\times 3) }^{ 8 }\\ { 48 }^{ 8 }={ 2 }^{ 32 }\times { 3 }^{ 8 }\\ \\ { 12 }^{ 8 }\times { 16 }^{ a }={ { (2 }^{ 2 }\times 3) }^{ 8 }\times { { (2 }^{ 4 }) }^{ a }\\ { 12 }^{ 8 }\times { 16 }^{ a }={ { 2 }^{ 16 }\times { 3 }^{ 8 } }\times { { 2 }^{ 4a } }\\ { 12 }^{ 8 }\times { 16 }^{ a }={ { 2 }^{ 16+4a }\times { 3 }^{ 8 } }\\ \\ { 2 }^{ 32 }\times { 3 }^{ 8 }={ { 2 }^{ 16+4a }\times { 3 }^{ 8 } }\\ \\ 32=16+4a\\ 32-16=4a\\ 16=4a\\ \boxed{a=4}$

48^8 = 12^8 x 16^a

(12x4)^8 = 12^8 x (4x4)^a

12^8 x 4^8 = 12^8 x 4^a x 4^a

4^8 = 4^2a

2a= 8

a= 8/2 = 4

since 48=4*12 than we satisfy 12^8 with 12^8 and we have left 4^8=16^a 16=4^2
4^8=4^2a 2a=8 result a=4

Divide the LHS and RHS by 12^8.Now 4^8 = 16^a => 4^8 = 4^2a => 2a=8 => a=4.

48^8 = 12^8 x 16^a

Rewrite

(3 x 2^4)^8 = (2^2 x 3)^8 x (2^4)^a

(3^8)(2^32) = (2^16)(3^8)(2^4a)

(3^8)(2^32) = (3^8)(2^(16+4a))

Equate the exponents of 2

32 = 16 + 4a

Solve for a

32 - 16 = 4a

16 = 4a

Divide both sides by 4

4 = a or a = 4

48^8 = 12^8*16^a or, 48^8/12^8 = 16^a or, (48/12)^8 = 16^a or, 4^8 = 4^2a or, 8 = 2a or, a = 4 (Ans)

48^8=12^8 * 16^a
=> (48^8) /(12^8) =16^a
=> {12^(4 8)/12^8}=16^a
=> 4^8=16^a
=> 4^(2

4)=16^a
=> 16^4=16^a
=> 4=a
=>a=4

Write a solution.

4^16x3^8= 4^8x3^8 +16^a = > 4^8=16^a=4^2a = > 2a=8 = > a=4

48^8=12^8*4^8 4^8=16^4 therefore a=4

48^8=48^4x16^a ^8=^4x16a 4a=16 a=4

12^8 × 4^8= 12^8×4^a×4^a 4^8=4^2a
8=2a a=4

48=12*4

so 48^8=12^8*(4)^8

but here we want 16^a

so4^8=(4^2)^(8/2)

4^8=16^4

48^8 = 12^8 * 16^a --> 48^8/12^8 = 16^a --> (48/12)^8 = 16^a --> 4^8 = 16^a --> 4^8 = 4^2a --> 8 = 2a.........................(If a^m = a^n then m = n) --> a = 4.

(16^8)/(12^8)=(16^a); 65536=(16^a); a=(log65536)/(log16); a=4

48^8=12^84^4a=)48^8=12^84^4*2 =)48^8=48^8

12*4=48.......so 12^8 *4^8 =48^8. Then 4^8 = 16^a. a=4

48^8=12^8 16^a (12 4)^8=12^8 16^a 12^8 4^8=12^8 16^a divide both sides by 12^8 12^8 4^8/12^8=12^8*16^a/12^8 then, 4^8=16^a express both sides with the same base(we can base it with 2 or 4, i choose 4) 4^8=4^2a equate the exponents, 2a=8 then divide both sides by 2 to get the value of a 2a/2=8/2 so, the value of a is 4....

12 16=192 means 192= 48^4, 12^8 16^8-4 so that 48^8=12^8*16^4

$48^8 = ((4)(12))^8=(4)^8(12)^8 = (12)^8(4)^{(2)(4)} = (12)^8(4^2)^4 = (12)^8(16)^4 = 12^816^a$

by observation, a = 4

(4^2 X 3)^8 = (4 X 3)^8 X 4^2a, 4^16 X 3^8 = 4^8 X 3^8 X 4^2a, Divide both sides by 3^8, 4^16 = 4^8 X 4^2a, 2a + 8 = 16, a = 4

48^8=12^8x16^a (48/12)^8=16^a 4^8=16^a 4^8=4^2a 8=2a a=4.

2^16 x 12^8=12^8 x 2^4a

2^16==2^4a

4a=16 a=4

48^8 = (12*4)^8 = 12^8 x 16^(1/2)^8 = 12^8 x 16^4

48^8/12^8=16^a 16^a=65536 16^a=16^4 a=4

48^8 = (12*4)^8 = 12^8 x 16^(1/2)^8 = 12^8 x 16^4

Another way to solve it (I think it's one of the more gradual and easier paths to use without calculating the results of the powers):

48^8 = 12^8 * 16^a <=>

<=> (4*12)^8 = 12^8 * 16^a <=>

<=> 12^8 * 4^8 = 12^8 * 16^a <=>

<=> 4^8 = 16^a <=>

<=> 4^8 = (4*4)^a <=>

<=> 4^8 = 4^a * 4^a <=>

<=> 4^8 = (4^a)^2 <=>

<=> 4^4 = (4^a) OR (-4)^4 = (4^a)

In both of those equations, a = 4, so that is the solution.

48^8=12^8 16^a (12 4)^8=12^8*16^a (4^2)^4=16^a a=4