Question:

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Options:
 A. 8.5 B. 13 C. 16 D. 17.5 E. None of these

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.

Then, $$\frac{(5^{2})^{7.5}\times (5)^{2.5}}{(5^{3})^{1.5}}$$  =5x

$$\frac{5^{(2\times7.5)}\times 5^{2.5}}{5^{(3\times1.5)}}$$ = 5x

$$\frac{5^{15}\times5^{2.5}}{5^{4.5}}$$  =  5x

5x = 5(15 + 2.5 - 4.5)

5x = 513

Therefore x = 13.

Check All Surds & Indices Questions (MCQs)

## More Questions Related to Quantitative Aptitude > Surds & Indices :

Question 1.

$$\frac{1}{1+x^{(b-a)}+x^{(c-a)}} +\frac{1}{1+x^{(a-b)}+x^{(c-b)}} + \frac{1}{1+x^{(b-c)}+x^{(a-c)}} = ?$$

Options:
1.    0
2.    1
3.    xa - b - c
4.    None of these

Given Exp. =  $$\frac{1}{\left(1+\frac{x^{b}}{x^{a}}+\frac{x^{c}}{x^{a}}\right)} +\frac{1}{\left(1+\frac{x^{a}}{x^{b}}+\frac{x^{c}}{x^{b}}\right)}+\frac{1}{\left(1+\frac{x^{b}}{x^{c}}+\frac{x^{a}}{x^{c}}\right)}$$

= $$\frac{x^{a}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{b}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{c}}{(x^{a}+x^{b}+x^{c})}$$

= $$\frac{(x^{a}+x^{b}+x^{c})}{(x^{a}+x^{b}+x^{c})}$$

= 1

Question 2.

The value of [(10)150 ÷ (10)146]

Options:
1.    1000
2.    10000
3.    100000
4.    106

(10)150 ÷ (10)146 = $$\frac{10^{150}}{10^{146}}$$

= 10150 - 146

= 104

= 10000.

Question 3.

(256)0.16 x (256)0.09 = ?

Options:
1.    4
2.    16
3.    64
4.    256.25

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)

= (256)0.25

= $$(256)^{\left(\frac{25}{100}\right)}$$

= $$(256)^{\left(\frac{1}{4}\right)}$$

= $$(4^{4})^{\left(\frac{1}{4}\right)}$$

= $$4^{4\left(\frac{1}{4}\right)}$$

= 41

= 4

Question 4.

(0.04)-1.5 = ?

Options:
1.    25
2.    125
3.    250
4.    625

(0.04)-1.5 =  $$\left(\frac{4}{100}\right)^{-1.5}$$

$$\left(\frac{1}{25}\right)^{-(\frac{3}{2})}$$

= $$\left(25\right)^{\left(\frac{3}{2}\right)}$$

= $$\left(5^{2}\right)^{\left(\frac{3}{2}\right)}$$

= $$\left(5\right)^{2\times\left(\frac{3}{2}\right)}$$

= 53

= 125.

Question 5.

$$\frac{\left(243\right)^{\frac{n}{5}}\times3^{2n+1}}{9^{n}\times3^{n-1}}= ?$$

Options:
1.    1
2.    2
3.    9
4.    3n

Given Expression = $$\frac{\left(243\right)^{\frac{n}{5}}\times3^{2n+1}}{9^{n}\times3^{n-1}}$$

= $$\frac{\left(3^{5}\right)^{\left(\frac{n}{5}\right)} \times3^{2n+1}}{\left(3^{2}\right)^{n}\times3^{n-1}}$$

= $$\frac{\left(3^{5\times(\frac{n}{5})}\times3^{2n-1}\right)}{\left(3^{2n}\times3^{n-1}\right)}$$

= $$\frac{3^{n}\times3^{2n-+1}}{3^{2n}\times3^{n-1}}$$

= $$\frac{3^{(n+2n+1)}}{3^{(2n+n-1)}}$$

= $$\frac{3^{3n+1}}{3^{3n-1}}$$

= 3(3n + 1 - 3n + 1)

= 32   = 9.

Question 6.

$$\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}} = ?$$

Options:
1.    0
2.    $$\frac{1}{2}$$
3.    1
4.    am + n
$$\frac{1}{1+a^{(n-m)}}+\frac{1}{1+a^{(m-n)}} = \frac{1}{\left(1+\frac{a^{n}}{a^{m}}\right)} + \frac{1}{\left(1+\frac{a^{m}}{a^{n}}\right)}$$
$$\frac{a^{m}}{\left(a^{m}+a^{n}\right)}+\frac{a^{n}}{\left(a^{m}+a^{n}\right)}$$
= $$\frac{{\left(a^{m}+a^{n}\right)}}{{\left(a^{m}+a^{n}\right)}}$$