Finite Math Examples

$4 x^{- \frac{43}{100}} = 24$

Step 1

Divide each term in $4 x^{- \frac{43}{100}} = 24$ by $4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $4 x^{- \frac{43}{100}} = 24$ by $4$ .

$\frac{4 x^{- \frac{43}{100}}}{4} = \frac{24}{4}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Move $x^{- \frac{43}{100}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4}{4 x^{\frac{43}{100}}} = \frac{24}{4}$

Step 1.2.2

Cancel the common factor.

$\frac{4}{4 x^{\frac{43}{100}}} = \frac{24}{4}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{x^{\frac{43}{100}}} = \frac{24}{4}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $24$ by $4$ .

$\frac{1}{x^{\frac{43}{100}}} = 6$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x^{\frac{43}{100}}, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x^{\frac{43}{100}}$

Step 3

Multiply each term in $\frac{1}{x^{\frac{43}{100}}} = 6$ by $x^{\frac{43}{100}}$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{1}{x^{\frac{43}{100}}} = 6$ by $x^{\frac{43}{100}}$ .

$\frac{1}{x^{\frac{43}{100}}} x^{\frac{43}{100}} = 6 x^{\frac{43}{100}}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $x^{\frac{43}{100}}$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{1}{x^{\frac{43}{100}}} x^{\frac{43}{100}} = 6 x^{\frac{43}{100}}$

Step 3.2.1.2

Rewrite the expression.

$1 = 6 x^{\frac{43}{100}}$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

Rewrite the equation as $6 x^{\frac{43}{100}} = 1$ .

$6 x^{\frac{43}{100}} = 1$

Step 4.2

Divide each term in $6 x^{\frac{43}{100}} = 1$ by $6$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $6 x^{\frac{43}{100}} = 1$ by $6$ .

$\frac{6 x^{\frac{43}{100}}}{6} = \frac{1}{6}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor.

$\frac{6 x^{\frac{43}{100}}}{6} = \frac{1}{6}$

Step 4.2.2.2

Divide $x^{\frac{43}{100}}$ by $1$ .

$x^{\frac{43}{100}} = \frac{1}{6}$

Step 4.3

Raise each side of the equation to the power of $\frac{100}{43}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{43}{100}})}^{\frac{100}{43}} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4

Simplify the exponent.

Tap for more steps...

Step 4.4.1

Simplify the left side.

Tap for more steps...

Step 4.4.1.1

Simplify ${(x^{\frac{43}{100}})}^{\frac{100}{43}}$ .

Tap for more steps...

Step 4.4.1.1.1

Multiply the exponents in ${(x^{\frac{43}{100}})}^{\frac{100}{43}}$ .

Tap for more steps...

Step 4.4.1.1.1.1

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

$x^{\frac{43}{100} \cdot \frac{100}{43}} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.1.1.1.2

Cancel the common factor of $43$ .

Tap for more steps...

Step 4.4.1.1.1.2.1

Cancel the common factor.

$x^{\frac{43}{100} \cdot \frac{100}{43}} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{100} \cdot 100} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.1.1.1.3

Cancel the common factor of $100$ .

Tap for more steps...

Step 4.4.1.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{100} \cdot 100} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.1.1.1.3.2

Rewrite the expression.

$x^{1} = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.1.1.2

Simplify.

$x = {(\frac{1}{6})}^{\frac{100}{43}}$

Step 4.4.2

Simplify the right side.

Tap for more steps...

Step 4.4.2.1

Simplify ${(\frac{1}{6})}^{\frac{100}{43}}$ .

Tap for more steps...

Step 4.4.2.1.1

Apply the product rule to $\frac{1}{6}$ .

$x = \frac{1^{\frac{100}{43}}}{6^{\frac{100}{43}}}$

Step 4.4.2.1.2

One to any power is one.

$x = \frac{1}{6^{\frac{100}{43}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{6^{\frac{100}{43}}}$

Decimal Form:

$x = 0.01550050 \dots$