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# What is the solution to equation 1 over the square root of 8 = 4^{(m + 2)}?

**Solution:**

Given, the equation is 1/√8 = 4^{(m + 2)}

When solving exponential equations, first we have to find a suitable common base.

Now, 8 = 2^{3} and 4 = 2^{2}

The above equation becomes 1/√2^{3} = 2^{2(m + 2)}

Using the property of powers

\(\sqrt[n]{a}\) = a^{1/n}

Now, 1/2^{3/2} = 2^{(2m + 4)}

Using the property, 1/a^{x} = a^{-x}

2^{-3/2} = 2^{2m + 4}

Now, we have the equality of 2 powers with an equal base.

We can write it as the equality of exponents as

-3/2 = 2m + 4

Grouping of common terms,

2m = -3/2 - 4

2m = (-3 - 8)/2

2m = -11/2

m = -11/4

m = -2 ¾

Therefore, the solution to the equation is -2 ¾

## What is the solution to equation 1 over the square root of 8 = 4^{(m + 2)}?

**Summary:**

The solution to equation 1 over the square root of 8 = 4^{(m + 2)} is -2 ¾

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