Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $12$ by $2$ .

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

Step 4.3

Subtract $4$ from $24$ .

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

Step 5

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

$x \cdot 10 = 20$

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $10$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $20$ by $10$ .

$x = 2$