Question

simplsimplifyand write in exponential form 2^-4 * 15^-3 * 625 / 5^2 * 10^-4

Answer 1

The answer is

$( \frac{5}{3} )^{3}$

GIVEN

Mathematical operation-

$\frac{ {2}^{ - 4} \times {15}^{ - 3} \times 625}{5 ^{2} \times {10}^{ - 4} }$

TO FIND

Simplify the given term.

SOLUTION

We can simply solve the above problem as follows;

$\frac{ {2}^{ - 4} \times {15}^{ - 3} \times 625}{5 ^{2} \times {10}^{ - 4} }$

Applying, a⁻ⁿ = 1/aⁿ

$= \frac{ {15}^{ - 3} \times 625 }{ {2}^{4} \times {5}^{2} \times {10}^{ - 4} }$

625 can be written as 5⁴

$= \frac{ {10}^{4} \times {5}^{4} }{ {2}^{4} \times {5}^{2} \times {15}^{3} }$

10⁴ can be written as (2×5)⁴

$= \frac{(2×5)^{4} \times {5}^{4} }{2 ^{4} \times {5}^{2} \times(3×5) ^{3} }$

Applying, aᵐ/aⁿ = aᵐ⁻ⁿ and (a×b)ⁿ = aⁿ × bⁿ

$= \frac{ {2}^{4 - 4} \times 5^{4} \times {5}^{4 - 2} }{ {3}^{3} \times {5}^{3} }$

$= \frac{ {2}^{0} \times {5}^{6 - 3}}{ {3}^{3} }$

We know that, a⁰ = 1

$= \frac{1 \times {5}^{3} }{3^{3} }$

Applying, aⁿ/bⁿ = (a/b)ⁿ

$= ( \frac{5}{3} )^{3}$

Hence, The answer is

$( \frac{5}{3})^{3}$

#Spj2

Answer 2

Answer:

The answer to the question is

${ (\frac{5}{3}) }^{3}$

Step-by-step explanation:

Given :

$\frac{ 2 ^{ - 4} * {15}^{ - 3} * 625 }{ 5^2 * {10}^{ - 4} }$

To find :

We have to simplify and write the exponential form of the above equation.

Solution :

The given expression is

$\frac{ 2 ^{ - 4} * {15}^{ - 3} * 625 }{ 5^2 * {10}^{ - 4} }$

we can apply the concept of

${a}^{ - m} = \frac{1}{ {a}^{m} }$

By applying this, the expression will become

$\frac{ {10}^{ 4} \times625 }{ {5}^{2} \times {2}^{4} \times {15}^{3} }$

The negative powers of the exponents are changed into a positive form.

$625 = {5}^{4}$

625 can be written in exponential form as the above.

let us substitute the value in the place of 625.

$\frac{ {10}^{4} \times {5}^{4} }{ {5}^{2} \times {2}^{4} \times {15}^{3} }$

The like terms will get cancelled.

$\frac{ {10}^{4} \times {5}^{2} }{ {2}^{4} \times {15}^{3} }$

The value 10 can be written as

${(x \times y)}^{m} = {x}^{m} \times {y}^{m}$

10 can be split as 5 and 2 as above.

$\frac{ {5}^{4} \times {2}^{4} \times {5}^{2} }{ {2}^{4} \times {15}^{3} }$

The like terms get cancelled, and the 15 split into 5 and 3 according to the above identity.

$\frac{ {5}^{4} \times {5}^{2} }{ {5}^{3} \times {3}^{3} } = \frac{ {5}^{6} }{ {5}^{3} \times {3}^{3} }$

The final answer will be

$\frac{ {5}^{3} }{ {3}^{3} }$

The simplified and exponential form of a given expression js

${( \frac{5}{3} )}^{3}$

# spj5