Algebra Examples

${(\frac{2 f^{3} t^{5}}{5 (f t^{5})})}^{0} \cdot (3 f^{4} t^{6})$

Step 1

Rewrite using the commutative property of multiplication.

$3 {(\frac{2 f^{3} t^{5}}{5 f t^{5}})}^{0} f^{4} t^{6}$

Step 2

Cancel the common factor of $f^{3}$ and $f$ .

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Step 2.1

Factor $f$ out of $2 f^{3} t^{5}$ .

$3 {(\frac{f (2 f^{2} t^{5})}{5 f t^{5}})}^{0} f^{4} t^{6}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $f$ out of $5 f t^{5}$ .

$3 {(\frac{f (2 f^{2} t^{5})}{f (5 t^{5})})}^{0} f^{4} t^{6}$

Step 2.2.2

Cancel the common factor.

$3 {(\frac{f (2 f^{2} t^{5})}{f (5 t^{5})})}^{0} f^{4} t^{6}$

Step 2.2.3

Rewrite the expression.

$3 {(\frac{2 f^{2} t^{5}}{5 t^{5}})}^{0} f^{4} t^{6}$

Step 3

Cancel the common factor of $t^{5}$ .

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Step 3.1

Cancel the common factor.

$3 {(\frac{2 f^{2} t^{5}}{5 t^{5}})}^{0} f^{4} t^{6}$

Step 3.2

Rewrite the expression.

$3 {(\frac{2 f^{2}}{5})}^{0} f^{4} t^{6}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{2 f^{2}}{5}$ .

$3 \frac{{(2 f^{2})}^{0}}{5^{0}} f^{4} t^{6}$

Step 4.2

Apply the product rule to $2 f^{2}$ .

$3 \frac{2^{0} {(f^{2})}^{0}}{5^{0}} f^{4} t^{6}$

Step 5

Simplify the numerator.

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Step 5.1

Anything raised to $0$ is $1$ .

$3 \frac{1 {(f^{2})}^{0}}{5^{0}} f^{4} t^{6}$

Step 5.2

Multiply the exponents in ${(f^{2})}^{0}$ .

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Step 5.2.1

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

$3 \frac{1 f^{2 \cdot 0}}{5^{0}} f^{4} t^{6}$

Step 5.2.2

Multiply $2$ by $0$ .

$3 \frac{1 f^{0}}{5^{0}} f^{4} t^{6}$

Step 5.3

Anything raised to $0$ is $1$ .

$3 \frac{1 \cdot 1}{5^{0}} f^{4} t^{6}$

Step 5.4

Multiply $1$ by $1$ .

$3 \frac{1}{5^{0}} f^{4} t^{6}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Anything raised to $0$ is $1$ .

$3 (\frac{1}{1}) f^{4} t^{6}$

Step 6.2

Cancel the common factor of $1$ .

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Step 6.2.1

Cancel the common factor.

$3 (\frac{1}{1}) f^{4} t^{6}$

Step 6.2.2

Rewrite the expression.

$3 \cdot 1 f^{4} t^{6}$

Step 6.3

Multiply $3$ by $1$ .

$3 f^{4} t^{6}$