Basic Math Examples

$k^{3} {(k^{\frac{7}{5}})}^{- 5}$

Step 1

Multiply the exponents in ${(k^{\frac{7}{5}})}^{- 5}$ .

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Step 1.1

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

$k^{3} k^{\frac{7}{5} \cdot - 5}$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Factor $5$ out of $- 5$ .

$k^{3} k^{\frac{7}{5} \cdot (5 (- 1))}$

Step 1.2.2

Cancel the common factor.

$k^{3} k^{\frac{7}{5} \cdot (5 \cdot - 1)}$

Step 1.2.3

Rewrite the expression.

$k^{3} k^{7 \cdot - 1}$

Step 1.3

Multiply $7$ by $- 1$ .

$k^{3} k^{- 7}$

Step 2

Multiply $k^{3}$ by $k^{- 7}$ by adding the exponents.

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Step 2.1

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

$k^{3 - 7}$

Step 2.2

Subtract $7$ from $3$ .

$k^{- 4}$

Step 3

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

$\frac{1}{k^{4}}$