Simplify (m^5)^2*(m^-3)^3

${(m^{5})}^{2} \cdot {(m^{- 3})}^{3}$

Step 1

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

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

$m^{5 \cdot 2} \cdot {(m^{- 3})}^{3}$

Multiply $5$ by $2$ .

$m^{10} \cdot {(m^{- 3})}^{3}$

Step 2

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

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

$m^{10} \cdot m^{- 3 \cdot 3}$

Multiply $- 3$ by $3$ .

$m^{10} \cdot m^{- 9}$

Step 3

Multiply $m^{10}$ by $m^{- 9}$ by adding the exponents.

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

$m^{10 - 9}$

Subtract $9$ from $10$ .

$m^{1}$

Step 4

Simplify $m^{1}$ .

$m$