Question

simplify. (1/2)^3×(3/4)^5×(4/6)^3. please give me a step by step explanation.​

Answer 1

Step-by-step explanation:

Given :-

(1/2)^3×(3/4)^5×(4/6)^3

To find:-

simplify. (1/2)^3×(3/4)^5×(4/6)^3

Solution:-

Given expression is (1/2)^3×(3/4)^5×(4/6)^3

=>[(1/2)^3×(4/6)^3]×(3/4)^5

=>[(1/2)^3×(2/3)^3]×(3/4)^5

we know that

a^m × b^m = (ab)^m

=>[(1/2)×(2/3)]^3 × (3/4)^5

=>(2/6)^3×(3/4)^5

=>(1/3)^3×(3/4)^5

we know that (a/b)^m = a^m /b^m

=>(1^3/3^3 )×(3^5 /5^5)

=>(1/3^3 )× (3^5/5^5)

3^5/(3^3×5^5)

=>(3^5/3^3)×(1/5^5)

we know that a^m/a^n = a^(m-n)

=>3^(5-3)/5^5

=>3^2/5^5

=>(3×3)/(5×5×5×5×5)

=>9/3125

Answer:-

The value of the given expression is 9/3125

Used formula:-

• a^m × b^m = (ab)^m

• (a/b)^m = a^m /b^m

• a^m/a^n = a^(m-n)