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Popular >

simplify (-5c^{-3})^4

Solution

simplify

(- 5 c^{- 3})^{4}

Solution

\frac{625}{c ^{12}}

Solution steps

(- 5 c^{- 3})^{4}

Apply exponent rule:

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

if

n

is even

(- 5 c^{- 3})^{4} = (5 c^{- 3})^{4}

= (5 c^{- 3})^{4}

Apply exponent rule:

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

(5 c^{- 3})^{4} = 5^{4} (c^{- 3})^{4}

= 5^{4} (c^{- 3})^{4}

5^{4} = 625

= 625 (c^{- 3})^{4}

Apply exponent rule:

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

assuming

a \geq 0

(c^{- 3})^{4} = c^{- 3 \cdot 4}

= 625 c^{- 3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= 625 c^{- 12}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

c^{- 12} = \frac{1}{c ^{12}}

= 625 \cdot \frac{1}{c ^{12}}

Simplify

625 \cdot \frac{1}{c ^{12}} : \frac{625}{c ^{12}}

= \frac{625}{c ^{12}}

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Frequently Asked Questions (FAQ)

What is (-5c^{-3})^4 ?
The solution to (-5c^{-3})^4 is (625)/(c^{12)}