Basic Math Examples

$(y + 9^{\frac{5}{2}}) - 1 = 31$

Step 1

Simplify $y + 9^{\frac{5}{2}} - 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $9$ as $3^{2}$ .

$y + {(3^{2})}^{\frac{5}{2}} - 1 = 31$

Step 1.1.2

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

$y + 3^{2 (\frac{5}{2})} - 1 = 31$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Cancel the common factor.

$y + 3^{2 (\frac{5}{2})} - 1 = 31$

Step 1.1.3.2

Rewrite the expression.

$y + 3^{5} - 1 = 31$

Step 1.1.4

Raise $3$ to the power of $5$ .

$y + 243 - 1 = 31$

Step 1.2

Subtract $1$ from $243$ .

$y + 242 = 31$

Step 2

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

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Step 2.1

Subtract $242$ from both sides of the equation.

$y = 31 - 242$

Step 2.2

Subtract $242$ from $31$ .

$y = - 211$