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Question 1 of 4
Simplify
`((m^2)/(3x^3))^2`
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Simplify the expression by using the Power of a Power.
$${\left(\frac{m^{\color{#007DDC}{2}}}{3x^{\color{#007DDC}{3}}}\right)}^\color{#9a00c7}{2}$$ |
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$$\frac{(m^{\color{#007DDC}{2}})^{\color{#9a00c7}{2}}}{(3x^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}}$$ |
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$$\frac{m^{\color{#007DDC}{2} \times \color{#9a00c7}{2}}}{3^{\color{#9a00c7}{2}}x^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}}$$ |
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`(m^4)/(9x^6)` |
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Question 2 of 4
Simplify
`((2a^3)/(5x))^2`
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Simplify the expression by using the Power of a Power.
$${\left(\frac{2a^{\color{#007DDC}{3}}}{5x}\right)}^\color{#9a00c7}{2}$$ |
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$$\frac{(2a^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}}{(5x)^{\color{#9a00c7}{2}}}$$ |
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$$\frac{2^{\color{#9a00c7}{2}}a^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}}{5^{\color{#9a00c7}{2}}x^{\color{#9a00c7}{2}}}$$ |
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`(4a^6)/(25x^2)` |
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Question 3 of 4
Simplify
`((2x^3)^2)/(8x^8-:2x^2)`
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First, use the Quotient of Powers to simplify the denominator.
$$\frac{(2x^3)^2}{8\color{#00880A}{x}^8 \div 2\color{#00880A}{x}^2}$$ |
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$$\frac{(2x^3)^2}{(8 \div 2) \times {\color{#00880A}{x}^{8-2}}}$$ |
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$$\frac{(2x^3)^2}{4 \times {\color{#00880A}{x}^6}}$$ |
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`((2x^3)^2)/(4x^6)` |
Simplify the expression further by using the Power of a Power.
$$\frac{(2x^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}}{4x^6}$$ |
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$$\frac{2^{\color{#9a00c7}{2}}x^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}}{4x^6}$$ |
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`(4x^6)/(4x^6)` |
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`1` |
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Question 4 of 4
Simplify
`((asqrtb)/(c^(-2)))^2-:((a^2 c^3)/b)^4`
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The equation can be written as a multiplication by getting the reciprocal of the divisor.
`((asqrtb)/(c^(-2)))^2-:((a^2 c^3)/b)^4` |
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`((asqrtb)/(c^(-2)))^2xx(b/(a^2 c^3))^4` |
Use Power of a Power to separate the numerator and denominator.
$$\left(\frac{a \sqrt{b}}{c^{\color{#007DDC}{-2}}}\right)^{\color{#9a00c7}{2}} \times \left(\frac{b}{a^2c^3}\right)^4$$ |
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$$\frac{a^{\color{#9a00c7}{2}} b^{\color{#007DDC}{\frac{1}{2}} \times \color{#9a00c7}{2}}}{c^{\color{#007DDC}{-2} \times \color{#9a00c7}{2}}} \times \left(\frac{b}{a^2c^3}\right)^4$$ |
`sqrtb=b^(1/2)` |
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$$\frac{a^2b^1}{c^{-4}} \times \left(\frac{b}{a^{\color{#007DDC}{2}}c^{\color{#007DDC}{3}}}\right)^{\color{#9a00c7}{4}}$$ |
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$$\frac{a^2b}{c^{-4}} \times \frac{b^{\color{#9a00c7}{4}}}{a^{\color{#007DDC}{2} \times \color{#9a00c7}{4}}c^{\color{#007DDC}{3} \times \color{#9a00c7}{4}}}$$ |
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`(a^2 b)/(c^(-4)) xx (b^4)/(a^8 c^(12))` |
Finally, use both Product and Quotient of Powers to simplify the equation further.
$$\frac{a^2\color{#00880A}{b}}{c^{-4}} \times \frac{\color{#00880A}{b}^4}{a^8 c^{12}}$$ |
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$$\frac{a^2\color{#00880A}{b}^{1+4}}{c^{-4} \times a^8 c^{12}}$$ |
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$$\frac{a^2 b^5}{\color{#00880A}{c}^{-4} \times a^8 \color{#00880A}{c}^{12}}$$ |
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$$\frac{a^2 b^5}{a^8 \color{#00880A}{c}^{-4+12}}$$ |
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$$\frac{a^2 b^5 \div \color{#CC0000}{a^2}}{a^8 c^8 \div \color{#CC0000}{a^2}}$$ |
Divide the numerator and the denominator by `a^2` |
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$$\frac{\color{#00880A}{a}^{2-2} b^5}{\color{#00880A}{a}^{8-2} c^8}$$ |
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$$\frac{b^5}{\color{#00880A}{a}^6 c^8}$$ |