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Popular >

simplify (2^0*x^{-3})^4

Solution

simplify

(2^{0} \cdot x^{- 3})^{4}

Solution

\frac{1}{x ^{12}}

Solution steps

(2^{0} x^{- 3})^{4}

Apply exponent rule:

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

(2^{0} x^{- 3})^{4} = (2^{0})^{4} (x^{- 3})^{4}

= (2^{0})^{4} (x^{- 3})^{4}

(2^{0})^{4} = 1

= 1 \cdot (x^{- 3})^{4}

Apply exponent rule:

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

assuming

a \geq 0

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

= 1 \cdot x^{- 3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= 1 \cdot x^{- 12}

Apply exponent rule:

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

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

= 1 \cdot \frac{1}{x ^{12}}

Multiply:

1 \cdot \frac{1}{x ^{12}} = \frac{1}{x ^{12}}

= \frac{1}{x ^{12}}

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Frequently Asked Questions (FAQ)

What is (2^0*x^{-3})^4 ?
The solution to (2^0*x^{-3})^4 is 1/(x^{12)}