Solve for x (r^(-5x^2-28))(r^9)=(r^(4x^2))/(r^100)

$(r^{- 5 x^{2} - 28}) (r^{9}) = \frac{r^{4 x^{2}}}{r^{100}}$

Move $r^{100}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$r^{- 5 x^{2} - 28} (r^{9}) = r^{4 x^{2}} r^{- 100}$

Multiply $r^{- 5 x^{2} - 28}$ by $r^{9}$ by adding the exponents.

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

$r^{- 5 x^{2} - 28 + 9} = r^{4 x^{2}} r^{- 100}$

Add $- 28$ and $9$ .

$r^{- 5 x^{2} - 19} = r^{4 x^{2}} r^{- 100}$

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

$r^{- 5 x^{2} - 19} = r^{4 x^{2} - 100}$

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

$- 5 x^{2} - 19 = 4 x^{2} - 100$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x^{2}$ from both sides of the equation.

$- 5 x^{2} - 19 - 4 x^{2} = - 100$

Subtract $4 x^{2}$ from $- 5 x^{2}$ .

$- 9 x^{2} - 19 = - 100$

Move all terms not containing $x$ to the right side of the equation.

Add $19$ to both sides of the equation.

$- 9 x^{2} = - 100 + 19$

Add $- 100$ and $19$ .

$- 9 x^{2} = - 81$

Divide each term in $- 9 x^{2} = - 81$ by $- 9$ and simplify.

Divide each term in $- 9 x^{2} = - 81$ by $- 9$ .

$\frac{- 9 x^{2}}{- 9} = \frac{- 81}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x^{2}}{- 9} = \frac{- 81}{- 9}$

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

$x^{2} = \frac{- 81}{- 9}$

Simplify the right side.

Divide $- 81$ by $- 9$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

Solve for x (r^(-5x^2-28))(r^9)=(r^(4x^2))/(r^100)

Related Questions

Support LCMGCF.com by disabling your adblocker.