Solve for x (p^(10x^2))/(p^(5x))=(p^-20)^x

$\frac{p^{10 x^{2}}}{p^{5 x}} = {(p^{- 20})}^{x}$

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

$\frac{p^{10 x^{2}}}{p^{5 x}} = p^{- 20 x}$

Move $p^{5 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$p^{10 x^{2}} p^{- 5 x} = p^{- 20 x}$

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

$p^{10 x^{2} - 5 x} = p^{- 20 x}$

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

$10 x^{2} - 5 x = - 20 x$

Solve for $x$ .

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

Add $20 x$ to both sides of the equation.

$10 x^{2} - 5 x + 20 x = 0$

Add $- 5 x$ and $20 x$ .

$10 x^{2} + 15 x = 0$

Factor $5 x$ out of $10 x^{2} + 15 x$ .

Factor $5 x$ out of $10 x^{2}$ .

$5 x (2 x) + 15 x = 0$

Factor $5 x$ out of $15 x$ .

$5 x (2 x) + 5 x (3) = 0$

Factor $5 x$ out of $5 x (2 x) + 5 x (3)$ .

$5 x (2 x + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$2 x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

The final solution is all the values that make $5 x (2 x + 3) = 0$ true.

$x = 0, - \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{3}{2}$

Decimal Form:

$x = 0, - 1.5$

Mixed Number Form:

$x = 0, - 1 \frac{1}{2}$

Solve for x (p^(10x^2))/(p^(5x))=(p^-20)^x

Related Questions

Support LCMGCF.com by disabling your adblocker.