Basic Math Examples

$9 y^{- 4} - 148^{- 2} + 64$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 \frac{1}{y^{4}} - 148^{- 2} + 64$

Step 1.2

Combine $9$ and $\frac{1}{y^{4}}$ .

$\frac{9}{y^{4}} - 148^{- 2} + 64$

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{9}{y^{4}} - \frac{1}{148^{2}} + 64$

Step 1.4

Raise $148$ to the power of $2$ .

$\frac{9}{y^{4}} - \frac{1}{21904} + 64$

Step 2

To write $\frac{9}{y^{4}}$ as a fraction with a common denominator, multiply by $\frac{21904}{21904}$ .

$\frac{9}{y^{4}} \cdot \frac{21904}{21904} - \frac{1}{21904} + 64$

Step 3

To write $- \frac{1}{21904}$ as a fraction with a common denominator, multiply by $\frac{y^{4}}{y^{4}}$ .

$\frac{9}{y^{4}} \cdot \frac{21904}{21904} - \frac{1}{21904} \cdot \frac{y^{4}}{y^{4}} + 64$

Step 4

Write each expression with a common denominator of $21904 y^{4}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{9}{y^{4}}$ by $\frac{21904}{21904}$ .

$\frac{9 \cdot 21904}{y^{4} \cdot 21904} - \frac{1}{21904} \cdot \frac{y^{4}}{y^{4}} + 64$

Step 4.2

Multiply $\frac{1}{21904}$ by $\frac{y^{4}}{y^{4}}$ .

$\frac{9 \cdot 21904}{y^{4} \cdot 21904} - \frac{y^{4}}{21904 y^{4}} + 64$

Step 4.3

Reorder the factors of $y^{4} \cdot 21904$ .

$\frac{9 \cdot 21904}{21904 y^{4}} - \frac{y^{4}}{21904 y^{4}} + 64$

Step 5

Combine into one fraction.

Tap for more steps...

Step 5.1

Combine the numerators over the common denominator.

$\frac{9 \cdot 21904 - y^{4}}{21904 y^{4}} + 64$

Step 5.2

Multiply $9$ by $21904$ .

$\frac{197136 - y^{4}}{21904 y^{4}} + 64$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Rewrite $197136$ as $444^{2}$ .

$\frac{444^{2} - y^{4}}{21904 y^{4}} + 64$

Step 6.2

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\frac{444^{2} - {(y^{2})}^{2}}{21904 y^{4}} + 64$

Step 6.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 444$ and $b = y^{2}$ .

$\frac{(444 + y^{2}) (444 - y^{2})}{21904 y^{4}} + 64$

Step 7

To write $64$ as a fraction with a common denominator, multiply by $\frac{21904 y^{4}}{21904 y^{4}}$ .

$\frac{(444 + y^{2}) (444 - y^{2})}{21904 y^{4}} + 64 \cdot \frac{21904 y^{4}}{21904 y^{4}}$

Step 8

Simplify terms.

Tap for more steps...

Step 8.1

Combine $64$ and $\frac{21904 y^{4}}{21904 y^{4}}$ .

$\frac{(444 + y^{2}) (444 - y^{2})}{21904 y^{4}} + \frac{64 (21904 y^{4})}{21904 y^{4}}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{(444 + y^{2}) (444 - y^{2}) + 64 (21904 y^{4})}{21904 y^{4}}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Expand $(444 + y^{2}) (444 - y^{2})$ using the FOIL Method.

Tap for more steps...

Step 9.1.1

Apply the distributive property.

$\frac{444 (444 - y^{2}) + y^{2} (444 - y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.1.2

Apply the distributive property.

$\frac{444 \cdot 444 + 444 (- y^{2}) + y^{2} (444 - y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.1.3

Apply the distributive property.

$\frac{444 \cdot 444 + 444 (- y^{2}) + y^{2} \cdot 444 + y^{2} (- y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2

Simplify and combine like terms.

Tap for more steps...

Step 9.2.1

Simplify each term.

Tap for more steps...

Step 9.2.1.1

Multiply $444$ by $444$ .

$\frac{197136 + 444 (- y^{2}) + y^{2} \cdot 444 + y^{2} (- y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.2

Multiply $- 1$ by $444$ .

$\frac{197136 - 444 y^{2} + y^{2} \cdot 444 + y^{2} (- y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.3

Move $444$ to the left of $y^{2}$ .

$\frac{197136 - 444 y^{2} + 444 \cdot y^{2} + y^{2} (- y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.4

Rewrite using the commutative property of multiplication.

$\frac{197136 - 444 y^{2} + 444 y^{2} - y^{2} y^{2} + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.5

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 9.2.1.5.1

Move $y^{2}$ .

$\frac{197136 - 444 y^{2} + 444 y^{2} - (y^{2} y^{2}) + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.5.2

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

$\frac{197136 - 444 y^{2} + 444 y^{2} - y^{2 + 2} + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.1.5.3

Add $2$ and $2$ .

$\frac{197136 - 444 y^{2} + 444 y^{2} - y^{4} + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.2

Add $- 444 y^{2}$ and $444 y^{2}$ .

$\frac{197136 + 0 - y^{4} + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.2.3

Add $197136$ and $0$ .

$\frac{197136 - y^{4} + 64 \cdot 21904 y^{4}}{21904 y^{4}}$

Step 9.3

Multiply $64$ by $21904$ .

$\frac{197136 - y^{4} + 1401856 y^{4}}{21904 y^{4}}$

Step 9.4

Add $- y^{4}$ and $1401856 y^{4}$ .

$\frac{197136 + 1401855 y^{4}}{21904 y^{4}}$

Step 9.5

Factor $3$ out of $197136 + 1401855 y^{4}$ .

Tap for more steps...

Step 9.5.1

Factor $3$ out of $197136$ .

$\frac{3 (65712) + 1401855 y^{4}}{21904 y^{4}}$

Step 9.5.2

Factor $3$ out of $1401855 y^{4}$ .

$\frac{3 (65712) + 3 (467285 y^{4})}{21904 y^{4}}$

Step 9.5.3

Factor $3$ out of $3 (65712) + 3 (467285 y^{4})$ .

$\frac{3 (65712 + 467285 y^{4})}{21904 y^{4}}$