Basic Math Examples

${(7 t^{- 3})}^{3} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 1

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

${(7 \frac{1}{t^{3}})}^{3} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 2

Combine $7$ and $\frac{1}{t^{3}}$ .

${(\frac{7}{t^{3}})}^{3} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{7}{t^{3}}$ .

$\frac{7^{3}}{{(t^{3})}^{3}} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 3.2

Raise $7$ to the power of $3$ .

$\frac{343}{{(t^{3})}^{3}} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 3.3

Multiply the exponents in ${(t^{3})}^{3}$ .

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Step 3.3.1

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

$\frac{343}{t^{3 \cdot 3}} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 3.3.2

Multiply $3$ by $3$ .

$\frac{343}{t^{9}} {(s^{5} t^{\frac{1}{4}})}^{2}$

Step 3.4

Apply the product rule to $s^{5} t^{\frac{1}{4}}$ .

$\frac{343}{t^{9}} ({(s^{5})}^{2} {(t^{\frac{1}{4}})}^{2})$

Step 3.5

Multiply the exponents in ${(s^{5})}^{2}$ .

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Step 3.5.1

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

$\frac{343}{t^{9}} (s^{5 \cdot 2} {(t^{\frac{1}{4}})}^{2})$

Step 3.5.2

Multiply $5$ by $2$ .

$\frac{343}{t^{9}} (s^{10} {(t^{\frac{1}{4}})}^{2})$

Step 3.6

Multiply the exponents in ${(t^{\frac{1}{4}})}^{2}$ .

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Step 3.6.1

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

$\frac{343}{t^{9}} (s^{10} t^{\frac{1}{4} \cdot 2})$

Step 3.6.2

Cancel the common factor of $2$ .

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Step 3.6.2.1

Factor $2$ out of $4$ .

$\frac{343}{t^{9}} (s^{10} t^{\frac{1}{2 (2)} \cdot 2})$

Step 3.6.2.2

Cancel the common factor.

$\frac{343}{t^{9}} (s^{10} t^{\frac{1}{2 \cdot 2} \cdot 2})$

Step 3.6.2.3

Rewrite the expression.

$\frac{343}{t^{9}} (s^{10} t^{\frac{1}{2}})$

Step 4

Cancel the common factor of $t^{\frac{1}{2}}$ .

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Step 4.1

Factor $t^{\frac{1}{2}}$ out of $t^{9}$ .

$\frac{343}{t^{\frac{1}{2}} t^{\frac{17}{2}}} (s^{10} t^{\frac{1}{2}})$

Step 4.2

Factor $t^{\frac{1}{2}}$ out of $s^{10} t^{\frac{1}{2}}$ .

$\frac{343}{t^{\frac{1}{2}} t^{\frac{17}{2}}} (t^{\frac{1}{2}} s^{10})$

Step 4.3

Cancel the common factor.

$\frac{343}{t^{\frac{1}{2}} t^{\frac{17}{2}}} (t^{\frac{1}{2}} s^{10})$

Step 4.4

Rewrite the expression.

$\frac{343}{t^{\frac{17}{2}}} s^{10}$

Step 5

Combine $\frac{343}{t^{\frac{17}{2}}}$ and $s^{10}$ .

$\frac{343 s^{10}}{t^{\frac{17}{2}}}$