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Popular >

simplify 2sqrt(4^{x^2-3x+2)}

Solution

simplify

2 4^{x^{2} - 3 x + 2}

Solution

2^{x^{2} - 3 x + 3}

Solution steps

2 4^{x^{2} - 3 x + 2}

4^{x^{2} - 3 x + 2} : 4^{\frac{x ^{2} - 3 x + 2}{2}}

= 2 \cdot 4^{\frac{x ^{2} - 3 x + 2}{2}}

Factor integer

4 = 2^{2}

= 2 (2^{2})^{\frac{x ^{2} - 3 x + 2}{2}}

Apply exponent rule:

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

(2^{2})^{\frac{x ^{2} - 3 x + 2}{2}} = 2^{2 \cdot \frac{x ^{2} - 3 x + 2}{2}}

= 2 \cdot 2^{2 \cdot \frac{x ^{2} - 3 x + 2}{2}}

Refine

= 2 \cdot 2^{x^{2} - 3 x + 2}

Apply exponent rule:

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

2 \cdot 2^{x^{2} - 3 x + 2} = 2^{1 + x^{2} - 3 x + 2}

= 2^{1 + x^{2} - 3 x + 2}

Simplify

1 + x^{2} - 3 x + 2 : x^{2} - 3 x + 3

= 2^{x^{2} - 3 x + 3}

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Frequently Asked Questions (FAQ)

What is 2sqrt(4^{x^2-3x+2)} ?
The solution to 2sqrt(4^{x^2-3x+2)} is 2^{x^2-3x+3}