Question

Write 2^-x × 3^-x × 6^2x × 3^2x × 2^2x as a power of 6

Answer 1

`6 {}^(3x)`

Explanation:

Given expression to us is ,

2^{-x} . 3^{-x} . 6^{2x} . 3^{2x} . 2^{2x}

We can rewrite it as ,

[2^{-x} . 2^{2x} ] [ 3^{-x} . 3^{2x}] . 6^{2x}

we know a^m . a^n = a^{m+n} , so ;

2^{-x +2x} . 3^{-x+2x} . 6^2x

simplify,

2^x . 3^x . 6^{2x}

we know a^m . b^m = (ab)^m , so ;

(2*3)^x . 6^{2x}

6^x . 6^2x

6^{x+2x}

6^{3x}

And we are done!

Answer 2

`6^(3x)`

Explanation:

Given exponential expression:

`2^(-x) \cdot 3^(-x) \cdot 6^(2x) \cdot 3^(2x) \cdot 2^(2x)`

`\textsf{Apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:`

`(2\cdot 3)^(-x) \cdot 6^(2x) \cdot (3 \cdot 2)^(2x)`

Multiply the numbers:

`6^(-x) \cdot 6^(2x) \cdot 6^(2x)`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`6^((-x+2x+2x))`

Therefore:

`6^(3x)`