Question

find the value of 4/(216)^-2/3 - 1/(256)^3/4

Answer 1

hope it will help you

Answer 2

Concept:

The following formulas are used for solving the given problem.

• (a^m)^n = a^mn

• 1/a^-n = a^n

Given:

The expression is 4/(216)^(-2/3) - 1/(256)^(3/4).

Find:

We have to find the value of the given expression.

Solution:

Write the given expression

4/(216)^(-2/3) - 1/(256)^(3/4)

We can write

4/(216)^(-2/3) = 4/(6³)^(-2/3)

Now, applying the formula (a^m)^n = a^mn in above

We get,

4/(216)^(-2/3) = 4/(6)^(-2×3/3)

4/(216)^(-2/3) = 4/(6)^(-2)

Using the formula 1/a^-n = a^n in the above equation

We get,

4/(216)^(-2/3) = 4 × 6²

4/(216)^(-2/3) = 4 × 36

4/(216)^(-2/3) = 144.......................(1)

Also, we can write

1/(256)^(3/4) = 1/(4^4)^(3/4)

Now, applying the formula (a^m)^n = a^mn in above

We get,

1/(256)^(3/4) = 1/(4)^(3×4/4)

1/(256)^(3/4) = 1/(4)^(3)

1/(256)^(3/4) = 1/64........................(2)

Now, subtract equation (2) from equation (1)

4/(216)^(-2/3) - 1/(256)^(3/4) = 144 - 1/64

4/(216)^(-2/3) - 1/(256)^(3/4) = (9216 - 1)/64

4/(216)^(-2/3) - 1/(256)^(3/4) = 9215/64

Hence, the value of 4/(216)^-2/3 - 1/(256)^3/4 is 9215/64.

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