Basic Math Examples

$\frac{4^{a + 6} - 4^{a + 2}}{4^{a + 1}}$

Step 1

Split the fraction $\frac{4^{a + 6} - 4^{a + 2}}{4^{a + 1}}$ into two fractions.

$\frac{4^{a + 6}}{4^{a + 1}} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 2

Cancel the common factor of $4^{a + 6}$ and $4^{a + 1}$ .

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Step 2.1

Factor $4^{a + 1}$ out of $4^{a + 6}$ .

$\frac{4^{a + 1} \cdot 4^{a + 6 - (a + 1)}}{4^{a + 1}} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{4^{a + 1} \cdot 4^{a + 6 - (a + 1)}}{4^{a + 1} \cdot 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 2.2.2

Cancel the common factor.

$\frac{4^{a + 1} \cdot 4^{a + 6 - (a + 1)}}{4^{a + 1} \cdot 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 2.2.3

Rewrite the expression.

$\frac{4^{a + 6 - (a + 1)}}{1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 2.2.4

Divide $4^{a + 6 - (a + 1)}$ by $1$ .

$4^{a + 6 - (a + 1)} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$4^{a + 6 - a - 1 \cdot 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 3.2

Multiply $- 1$ by $1$ .

$4^{a + 6 - a - 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 4

Simplify terms.

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Step 4.1

Combine the opposite terms in $a + 6 - a - 1$ .

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Step 4.1.1

Subtract $a$ from $a$ .

$4^{0 + 6 - 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 4.1.2

Add $0$ and $6$ .

$4^{6 - 1} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Subtract $1$ from $6$ .

$4^{5} + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 4.2.2

Raise $4$ to the power of $5$ .

$1024 + \frac{- 4^{a + 2}}{4^{a + 1}}$

Step 4.3

Cancel the common factor of $4^{a + 2}$ and $4^{a + 1}$ .

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Step 4.3.1

Factor $4^{a + 1}$ out of $- 4^{a + 2}$ .

$1024 + \frac{4^{a + 1} (- 4^{a + 2 - (a + 1)})}{4^{a + 1}}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Multiply by $1$ .

$1024 + \frac{4^{a + 1} (- 4^{a + 2 - (a + 1)})}{4^{a + 1} \cdot 1}$

Step 4.3.2.2

Cancel the common factor.

$1024 + \frac{4^{a + 1} (- 4^{a + 2 - (a + 1)})}{4^{a + 1} \cdot 1}$

Step 4.3.2.3

Rewrite the expression.

$1024 + \frac{- 4^{a + 2 - (a + 1)}}{1}$

Step 4.3.2.4

Divide $- 4^{a + 2 - (a + 1)}$ by $1$ .

$1024 - 4^{a + 2 - (a + 1)}$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$1024 - 4^{a + 2 - a - 1 \cdot 1}$

Step 5.2

Multiply $- 1$ by $1$ .

$1024 - 4^{a + 2 - a - 1}$

Step 6

Simplify by adding terms.

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Step 6.1

Combine the opposite terms in $a + 2 - a - 1$ .

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Step 6.1.1

Subtract $a$ from $a$ .

$1024 - 4^{0 + 2 - 1}$

Step 6.1.2

Add $0$ and $2$ .

$1024 - 4^{2 - 1}$

Step 6.2

Subtract $1$ from $2$ .

$1024 - 4^{1}$

Step 7

Evaluate the exponent.

$1024 - 1 \cdot 4$

Step 8

Multiply $- 1$ by $4$ .

$1024 - 4$

Step 9

Subtract $4$ from $1024$ .

$1020$