Algebra Examples

${(y^{b})}^{4} = \frac{1}{y^{24}}$

Step 1

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

$y^{b \cdot 4} = \frac{1}{y^{24}}$

Step 2

Move $y^{24}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y^{b \cdot 4} = y^{- 24}$

Step 3

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

$b \cdot 4 = - 24$

Step 4

Divide each term in $b \cdot 4 = - 24$ by $4$ and simplify.

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Step 4.1

Divide each term in $b \cdot 4 = - 24$ by $4$ .

$\frac{b \cdot 4}{4} = \frac{- 24}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{b \cdot 4}{4} = \frac{- 24}{4}$

Step 4.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 24}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 24$ by $4$ .

$b = - 6$

Step 5

To rewrite as a function of $y$ , write the equation so that $b$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = - 6$