Algebra Examples

$3 - 1 (25^{\frac{1}{2}} - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $25$ as $5^{2}$ .

$3 - 1 ({(5^{2})}^{\frac{1}{2}} - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.2

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

$3 - 1 (5^{2 (\frac{1}{2})} - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Cancel the common factor.

$3 - 1 (5^{2 (\frac{1}{2})} - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.3.2

Rewrite the expression.

$3 - 1 (5^{1} - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.4

Evaluate the exponent.

$3 - 1 (5 - 8^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.5

Rewrite $8$ as $2^{3}$ .

$3 - 1 (5 - {(2^{3})}^{\frac{1}{3}}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.6

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

$3 - 1 (5 - 2^{3 (\frac{1}{3})}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.7

Cancel the common factor of $3$ .

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Step 1.1.7.1

Cancel the common factor.

$3 - 1 (5 - 2^{3 (\frac{1}{3})}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.7.2

Rewrite the expression.

$3 - 1 (5 - 2^{1}) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.8

Evaluate the exponent.

$3 - 1 (5 - 1 \cdot 2) (4^{\frac{1}{2}} + 27^{0})$

Step 1.1.9

Multiply $- 1$ by $2$ .

$3 - 1 (5 - 2) (4^{\frac{1}{2}} + 27^{0})$

Step 1.2

Subtract $2$ from $5$ .

$3 - 1 \cdot 3 (4^{\frac{1}{2}} + 27^{0})$

Step 1.3

Multiply $- 1$ by $3$ .

$3 - 3 (4^{\frac{1}{2}} + 27^{0})$

Step 1.4

Simplify each term.

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Step 1.4.1

Rewrite $4$ as $2^{2}$ .

$3 - 3 ({(2^{2})}^{\frac{1}{2}} + 27^{0})$

Step 1.4.2

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

$3 - 3 (2^{2 (\frac{1}{2})} + 27^{0})$

Step 1.4.3

Cancel the common factor of $2$ .

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Step 1.4.3.1

Cancel the common factor.

$3 - 3 (2^{2 (\frac{1}{2})} + 27^{0})$

Step 1.4.3.2

Rewrite the expression.

$3 - 3 (2^{1} + 27^{0})$

Step 1.4.4

Evaluate the exponent.

$3 - 3 (2 + 27^{0})$

Step 1.4.5

Anything raised to $0$ is $1$ .

$3 - 3 (2 + 1)$

Step 1.5

Add $2$ and $1$ .

$3 - 3 \cdot 3$

Step 1.6

Multiply $- 3$ by $3$ .

$3 - 9$

Step 2

Subtract $9$ from $3$ .

$- 6$