Simplify y^5y^3-(y^-2)^4

$y^{5} y^{3} - {(y^{- 2})}^{4}$

Step 1

Multiply $y^{5}$ by $y^{3}$ by adding the exponents.

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

$y^{5 + 3} - {(y^{- 2})}^{4}$

Add $5$ and $3$ .

$y^{8} - {(y^{- 2})}^{4}$

Step 2

Multiply the exponents in ${(y^{- 2})}^{4}$ .

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

$y^{8} - y^{- 2 \cdot 4}$

Multiply $- 2$ by $4$ .

$y^{8} - y^{- 8}$

Step 3

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

$y^{8} - \frac{1}{y^{8}}$