The correct option is D 1 Given, (m^3+2^3+3^3)^ 5/2=6^ 5 taking power of 2/5 on both sides, we get, ((m^3+2^3+3^3)^ 5/2)^ 2/5=(6^ 5)^ 2/5 ...

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If m3+23+33...

Question

If $(m^{3} + 2^{3} + 3^{3})^{- \frac{5}{2}} = (6)^{- 5}$

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Solution

The correct option is D $1$
Given,

${(m^{3} + 2^{3} + 3^{3})}^{- \frac{5}{2}} = 6^{- 5}$

taking power of $- \frac{2}{5}$ on both sides, we get,

${({(m^{3} + 2^{3} + 3^{3})}^{- \frac{5}{2}})}^{\frac{- 2}{5}} = {(6^{- 5})}^{\frac{- 2}{5}}$

$(m^{3} + 2^{3} + 3^{3}) = 36$

$m^{3} + 8 + 27 = 36$

$m^{3} + 35 = 36$

$m^{3} = 36 - 35 = 1$

$∴ m = 1$

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Similar questions

(m^{3} + 2^{3} + 3^{3})^{- \frac{5}{2}} = (6)^{- 5}

m

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + \cdot \cdot \cdot + \frac{1^{3} + 2^{3} + 3^{3} + \cdot \cdot \cdot + 15^{3}}{1 + 2 + 3 + \cdot \cdot \cdot + 15} - \frac{1}{2} (1 + 2 + 3 + \cdot \cdot \cdot + 15)

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + \cdot \cdot \cdot + \frac{1^{3} + 2^{3} + 3^{3} + \cdot \cdot \cdot + 15^{3}}{1 + 2 + 3 + \cdot \cdot \cdot + 15} - \frac{1}{2} (1 + 2 + 3 + \cdot \cdot \cdot + 15)

Simplify:

(1)

(2)

(3)

(4)

(5)

(6)

\frac{2}{3}

\frac{2 + 3}{3 + 3}

\frac{2 - 1}{3 - 1}

\frac{2 \times 5}{3 \times 5}

\frac{2 + 5}{3 + 5}

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