simplify (-5a^3)^5

Solution

simplify

(- 5 a^{3})^{5}

- 3125 a^{15}

Solution steps

(- 5 a^{3})^{5}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 5 a^{3})^{5} = - (5 a^{3})^{5}

= - (5 a^{3})^{5}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(5 a^{3})^{5} = 5^{5} (a^{3})^{5}

= - 5^{5} (a^{3})^{5}

5^{5} = 3125

= - 3125 (a^{3})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(a^{3})^{5} = a^{3 \cdot 5}

= - 3125 a^{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= - 3125 a^{15}

(1 + w^{2})^{4}

\frac{- 3.2 x + 31.68 + 4 y + 5 x}{4}

x^{4} - 14 x^{2} y^{2} - 51 y^{4}

x^{109} \cdot 2 \cdot 10 x^{5} x^{1045} \cdot 10 - 2 x^{10}

(\frac{1}{4 m})^{- 3}