Basic Math Examples

$\frac{{(- 2)}^{4 y + 2}}{{(- 2)}^{2 y}} = {(- 2)}^{12}$

Step 1

Move ${(- 2)}^{2 y}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(- 2)}^{4 y + 2} {(- 2)}^{- 2 y} = {(- 2)}^{12}$

Step 2

Multiply ${(- 2)}^{4 y + 2}$ by ${(- 2)}^{- 2 y}$ by adding the exponents.

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Step 2.1

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

${(- 2)}^{4 y + 2 - 2 y} = {(- 2)}^{12}$

Step 2.2

Subtract $2 y$ from $4 y$ .

${(- 2)}^{2 y + 2} = {(- 2)}^{12}$

Step 3

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

$2 y + 2 = 12$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $2$ from both sides of the equation.

$2 y = 12 - 2$

Step 4.1.2

Subtract $2$ from $12$ .

$2 y = 10$

Step 4.2

Divide each term in $2 y = 10$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 y = 10$ by $2$ .

$\frac{2 y}{2} = \frac{10}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{10}{2}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $10$ by $2$ .

$y = 5$