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Popular >

simplify 128^{1/4}

Solution

simplify

12 8^{\frac{1}{4}}

Solution

2 \cdot 2^{\frac{3}{4}}

+1

Decimal Notation

3.36358 \dots

Solution steps

12 8^{\frac{1}{4}}

Prime factorization of

128 : 2^{7}

= (2^{7})^{\frac{1}{4}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{7} = 2^{4} \cdot 2^{3}

= (2^{4} \cdot 2^{3})^{\frac{1}{4}}

Apply exponent rule:

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

(2^{4} \cdot 2^{3})^{\frac{1}{4}} = (2^{4})^{\frac{1}{4}} (2^{3})^{\frac{1}{4}}

= (2^{4})^{\frac{1}{4}} (2^{3})^{\frac{1}{4}}

(2^{4})^{\frac{1}{4}} = 2

= 2 (2^{3})^{\frac{1}{4}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(2^{3})^{\frac{1}{4}} = 2^{3 \cdot \frac{1}{4}}

= 2 \cdot 2^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= 2 \cdot 2^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is 128^{1/4} ?
The solution to 128^{1/4} is 2*2^{3/4}