Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine.

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

Step 5

Multiply $s$ by $1$ .

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

Step 6

Combine $t^{3}$ and $\frac{1}{s^{4}}$ .

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

Step 7

Multiply the numerator by the reciprocal of the denominator.

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

Step 8

Multiply $s \frac{s^{4}}{t^{3}}$ .

Tap for more steps...

Step 8.1

Combine $s$ and $\frac{s^{4}}{t^{3}}$ .

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

Step 8.2

Multiply $s$ by $s^{4}$ by adding the exponents.

Tap for more steps...

Step 8.2.1

Multiply $s$ by $s^{4}$ .

Tap for more steps...

Step 8.2.1.1

Raise $s$ to the power of $1$ .

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

Step 8.2.1.2

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

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

Step 8.2.2

Add $1$ and $4$ .

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

Step 9

Apply the product rule to $\frac{s^{5}}{t^{3}}$ .

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

Step 10

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

Tap for more steps...

Step 10.1

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

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

Step 10.2

Multiply $5$ by $2$ .

$\frac{s^{10}}{{(t^{3})}^{2}}$

Step 11

Multiply the exponents in ${(t^{3})}^{2}$ .

Tap for more steps...

Step 11.1

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

$\frac{s^{10}}{t^{3 \cdot 2}}$

Step 11.2

Multiply $3$ by $2$ .

$\frac{s^{10}}{t^{6}}$