Find 5-4- 1255-3- 25-1-2

5 ^ 4 × (125) ^ 5 3 #160; ⇒ 5 ^ 4 × 5 ^ 5 =5 Now , #160; 5÷( 25 ) #160; ^ 1 2 #160; ⇒ 5 ( 5 ) #160; ^ 1 2 × 2 = 5 ...

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Byju's Answer

Standard X

Mathematics

Rational Expression

Find 5-4× 1...

Question

Find $5^{- 4} \times (125)^{\frac{5}{3}} \div (25)^{- \frac{1}{2}}$

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Solution

$5^{- 4} \times {(125)}^{\frac{5}{3}} \Rightarrow 5^{- 4} \times 5^{5} = 5$
Now $,$
$5 \div {(25)}^{- \frac{1}{2}} \Rightarrow \frac{5}{{(5)}^{- \frac{1}{2} \times 2}} = \frac{5}{5^{- 1}} = 25.$

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Similar questions

Q. Evaluate

5^{- 4} \times (125)^{\frac{5}{3}} \div (25)^{\frac{- 1}{2}}

Find the odd-one-out from the alternatives.

(1)

25, 5, 5

(2)

51, 3, 17

(3)

96, 6, 16

(4)

75, 5, 25

Simplify : 25-1/2{5+4-(3+2-1+3)}

Find x, if

$(i) {(\frac{1}{4})}^{- 4} \times {(\frac{1}{4})}^{- 8} = {(\frac{1}{4})}^{- 4 x} (i i) {(\frac{- 1}{2})}^{- 19} \div {(\frac{- 1}{2})}^{8} = {(\frac{- 1}{2})}^{- 2 x + 1} (i i i) {(\frac{3}{2})}^{- 3} \div {(\frac{3}{2})}^{5} = {(\frac{3}{2})}^{2 x + 1} (i v) {(\frac{2}{5})}^{- 3} \times {(\frac{2}{5})}^{15} = {(\frac{2}{5})}^{2 + 3 x} (v) {(\frac{5}{4})}^{- x} \div {(\frac{5}{4})}^{- 4} = {(\frac{5}{4})}^{5} (v i) {(\frac{8}{3})}^{2 x + 1} \times {(\frac{8}{3})}^{5} = {(\frac{8}{3})}^{x + 2}$

Q. If

\frac{25}{k} = 1^{2} - \frac{2^{2}}{5} + \frac{3^{2}}{5^{2}} - \frac{4^{2}}{5^{3}} + \frac{5^{2}}{5^{4}} - \frac{6^{2}}{5^{2}} + . . . . . . \infty

, then find the value of

k

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Find 5−4×(125)53÷(25)−12

5−4×(125)53⇒5−4×55=5Now, 5÷(25)−12⇒5(5)−12×2=55−1=25.

Find $5^{- 4} \times (125)^{\frac{5}{3}} \div (25)^{- \frac{1}{2}}$

$5^{- 4} \times {(125)}^{\frac{5}{3}} \Rightarrow 5^{- 4} \times 5^{5} = 5$
Now $,$
$5 \div {(25)}^{- \frac{1}{2}} \Rightarrow \frac{5}{{(5)}^{- \frac{1}{2} \times 2}} = \frac{5}{5^{- 1}} = 25.$