Solve for x (6^x)^10=((6^12)^2)/(6^4)

${(6^{x})}^{10} = \frac{{(6^{12})}^{2}}{6^{4}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6^{x \cdot 10} = \frac{{(6^{12})}^{2}}{6^{4}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6^{x \cdot 10} = \frac{6^{12 \cdot 2}}{6^{4}}$

Move $6^{4}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$6^{x \cdot 10} = 6^{12 \cdot 2} \cdot 6^{- 4}$

Multiply $6^{12 \cdot 2}$ by $6^{- 4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6^{x \cdot 10} = 6^{12 \cdot 2 - 4}$

Multiply $12$ by $2$ .

$6^{x \cdot 10} = 6^{24 - 4}$

Subtract $4$ from $24$ .

$6^{x \cdot 10} = 6^{20}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x \cdot 10 = 20$

Divide each term in $(x \cdot 10) = 20$ by $10$ and simplify.

Divide each term in $(x \cdot 10) = 20$ by $10$ .

$\frac{(x \cdot 10)}{10} = \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{x \cdot 10}{10} = \frac{20}{10}$

Divide $x$ by $1$ .

$x = \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$x = 2$