Evaluate (10x/6)(10x/8)=10^10

$(10 \frac{x}{6}) (10 \frac{x}{8}) = 10^{10}$

Step 1

Simplify.

Combine $10$ and $\frac{x}{6}$ .

$\frac{10 x}{6} \cdot (10 (\frac{x}{8})) = 10^{10}$

Combine $10$ and $\frac{x}{8}$ .

$\frac{10 x}{6} \cdot \frac{10 x}{8} = 10^{10}$

Multiply $\frac{10 x}{6}$ by $\frac{10 x}{8}$ .

$\frac{10 x (10 x)}{6 \cdot 8} = 10^{10}$

Multiply $10$ by $10$ .

$\frac{100 x \cdot x}{6 \cdot 8} = 10^{10}$

Raise $x$ to the power of $1$ .

$\frac{100 (x^{1} x)}{6 \cdot 8} = 10^{10}$

Raise $x$ to the power of $1$ .

$\frac{100 (x^{1} x^{1})}{6 \cdot 8} = 10^{10}$

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

$\frac{100 x^{1 + 1}}{6 \cdot 8} = 10^{10}$

Add $1$ and $1$ .

$\frac{100 x^{2}}{6 \cdot 8} = 10^{10}$

Multiply $6$ by $8$ .

$\frac{100 x^{2}}{48} = 10^{10}$

Step 2

Divide each term in $\frac{100 x^{2}}{48} = 10^{10}$ by $100$ and simplify.

Divide each term in $\frac{100 x^{2}}{48} = 10^{10}$ by $100$ .

$\frac{\frac{100 x^{2}}{48}}{100} = \frac{10^{10}}{100}$

Simplify the left side.

Cancel the common factor of $100$ and $48$ .

Factor $4$ out of $100 x^{2}$ .

$\frac{\frac{4 (25 x^{2})}{48}}{100} = \frac{10^{10}}{100}$

Cancel the common factors.

Factor $4$ out of $48$ .

$\frac{\frac{4 (25 x^{2})}{4 (12)}}{100} = \frac{10^{10}}{100}$

Cancel the common factor.

$\frac{\frac{4 (25 x^{2})}{4 \cdot 12}}{100} = \frac{10^{10}}{100}$

Rewrite the expression.

$\frac{\frac{25 x^{2}}{12}}{100} = \frac{10^{10}}{100}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{25 x^{2}}{12} \cdot \frac{1}{100} = \frac{10^{10}}{100}$

Combine.

$\frac{25 x^{2} \cdot 1}{12 \cdot 100} = \frac{10^{10}}{100}$

Cancel the common factor of $25$ and $100$ .

Factor $25$ out of $25 x^{2} \cdot 1$ .

$\frac{25 (x^{2} \cdot 1)}{12 \cdot 100} = \frac{10^{10}}{100}$

Cancel the common factors.

Factor $25$ out of $12 \cdot 100$ .

$\frac{25 (x^{2} \cdot 1)}{25 (12 \cdot 4)} = \frac{10^{10}}{100}$

Cancel the common factor.

$\frac{25 (x^{2} \cdot 1)}{25 (12 \cdot 4)} = \frac{10^{10}}{100}$

Rewrite the expression.

$\frac{x^{2} \cdot 1}{12 \cdot 4} = \frac{10^{10}}{100}$

Multiply.

Multiply $x^{2}$ by $1$ .

$\frac{x^{2}}{12 \cdot 4} = \frac{10^{10}}{100}$

Multiply $12$ by $4$ .

$\frac{x^{2}}{48} = \frac{10^{10}}{100}$

Simplify the right side.

Raise $10$ to the power of $10$ .

$\frac{x^{2}}{48} = \frac{10000000000}{100}$

Divide $10000000000$ by $100$ .

$\frac{x^{2}}{48} = 100000000$

Step 3

Multiply both sides of the equation by $48$ .

$48 \frac{x^{2}}{48} = 48 \cdot 100000000$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $48$ .

Cancel the common factor.

$48 \frac{x^{2}}{48} = 48 \cdot 100000000$

Rewrite the expression.

$x^{2} = 48 \cdot 100000000$

Simplify the right side.

Multiply $48$ by $100000000$ .

$x^{2} = 4800000000$

Step 5

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{4800000000}$

Step 6

Simplify $\pm \sqrt{4800000000}$ .

Rewrite $4800000000$ as $40000^{2} \cdot 3$ .

Factor $1600000000$ out of $4800000000$ .

$x = \pm \sqrt{1600000000 (3)}$

Rewrite $1600000000$ as $40000^{2}$ .

$x = \pm \sqrt{40000^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 40000 \sqrt{3}$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 40000 \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 40000 \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 40000 \sqrt{3}, - 40000 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 40000 \sqrt{3}, - 40000 \sqrt{3}$

Decimal Form:

$x = 69282.03230275 \dots, - 69282.03230275 \dots$

Evaluate (10x/6)(10x/8)=10^10

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