Simplify- 5-1- 7252 - 7-47-2-52 - 7353 - 7-5-5-2-

5^( 1 2)×(7/2) + (2 3) ×(5/2)_ × 7^2 4×(7/2)+(3+5) × ( 5/2)_ = 75^8_ = 7390625 ...

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Byju's Answer

Standard VII

Mathematics

Power of a Power

Simplify: 5-...

Question

Simplify:
${(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{7 / 2} \times {(\frac{5^{2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{- 5 / 2}$ .

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Solution

$5^{(- 1 - 2) \times (7 / 2) + (2 - 3) \times (5 / 2)}$ $\times$ $7^{2 - 4 \times (7 / 2) + (3 + 5) \times (- 5 / 2)}$
= $\frac{7}{5^{8}}$
= $\frac{7}{390625}$

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Similar questions

{(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{4}})}^{\frac{7}{2}} \times {(\frac{5^{- 2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{\frac{- 5}{2}}

Simplify:

(i) $(16^{\frac{- 1}{5}})^{\frac{5}{2}}$

(ii) $\sqrt[5]{(32)^{- 3}}$

(iii) $\sqrt[3]{(343)^{- 2}}$

(iv) $(0.001)^{\frac{1}{3}}$

(v) $\frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}$

(vi) ${(\frac{\sqrt{2}}{5})}^{8} \div {(\frac{\sqrt{2}}{5})}^{13}$

(vii) ${(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{\frac{7}{2}} \times {(\frac{5^{- 2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{\frac{- 5}{2}}$

Q. Simplify by rationalizing the denominator

(i)

\frac{4}{\sqrt{7} + \sqrt{3}}

(ii)

\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}}

(iii)

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

(iv)

\frac{2 \sqrt{3} - \sqrt{2}}{2 \sqrt{2} + 3 \sqrt{3}}

(v)

\frac{7 \sqrt{3} - 5 \sqrt{2}}{\sqrt{48} + \sqrt{18}}

(vi)

\frac{x + 9}{\sqrt{x + 9}}

(vii)

\frac{1}{{(3 + \sqrt{5})}^{2}} + \frac{1}{{(3 - \sqrt{5})}^{2}}

(5-¹×7²÷5²×7-⁴)-7/2 × (5^{-²×7³÷ 5³×7to the power -5) -5/2}

Q. Simplify:

{[{(3^{5 / 2} \times 5^{3 / 4}) \div 2^{- 5 / 4}} \div {16 \div (5^{2} \times 2^{1 / 4} \times 3^{1 / 2})}]}^{1 / 5}

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Simplify:(5−1×7252×7−4)7/2×(52×7353×7−5)−5/2.

5(−1−2)×(7/2)+(2−3)×(5/2) × 72−4×(7/2)+(3+5)×(−5/2)= 758= 7390625

Simplify:
${(\frac{5^{- 1} \times 7^{2}}{5^{2} \times 7^{- 4}})}^{7 / 2} \times {(\frac{5^{2} \times 7^{3}}{5^{3} \times 7^{- 5}})}^{- 5 / 2}$ .

$5^{(- 1 - 2) \times (7 / 2) + (2 - 3) \times (5 / 2)}$ $\times$ $7^{2 - 4 \times (7 / 2) + (3 + 5) \times (- 5 / 2)}$
= $\frac{7}{5^{8}}$
= $\frac{7}{390625}$