Solve for x 4^(9-6x)=(1/64)^(10/3)

$4^{9 - 6 x} = {(\frac{1}{64})}^{\frac{10}{3}}$

Step 1

Apply the product rule to $\frac{1}{64}$ .

$4^{9 - 6 x} = \frac{1^{\frac{10}{3}}}{64^{\frac{10}{3}}}$

Step 2

One to any power is one.

$4^{9 - 6 x} = \frac{1}{64^{\frac{10}{3}}}$

Step 3

Move $64^{\frac{10}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{9 - 6 x} = 64^{- \frac{10}{3}}$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$4^{9 - 6 x} = 4^{3 (- \frac{10}{3})}$

Step 5

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

$9 - 6 x = 3 (- \frac{10}{3})$

Step 6

Solve for $x$ .

Simplify $3 (- \frac{10}{3})$ .

Rewrite.

$9 - 6 x = 0 + 0 + 3 (- \frac{10}{3})$

Simplify by adding zeros.

$9 - 6 x = 3 (- \frac{10}{3})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$9 - 6 x = 3 (\frac{- 10}{3})$

Cancel the common factor.

$9 - 6 x = 3 (\frac{- 10}{3})$

Rewrite the expression.

$9 - 6 x = - 10$

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

Subtract $9$ from both sides of the equation.

$- 6 x = - 10 - 9$

Subtract $9$ from $- 10$ .

$- 6 x = - 19$

Divide each term in $- 6 x = - 19$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 19$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 19}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 19}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 19}{- 6}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{19}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{6}$

Decimal Form:

$x = 3.1\overline{6}$

Mixed Number Form:

$x = 3 \frac{1}{6}$

Solve for x 4^(9-6x)=(1/64)^(10/3)

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