We know that exponents raised to the negative power will generate fractions. 

We also know that \(\displaystyle 8\) is divisible by \(\displaystyle 2\).

\(\displaystyle 8=2^3\) 

However, since this a fraction, we then have the following:

\(\displaystyle \frac{1}{8}=2^{-3}\). 

If fractions are raised to a positive integer exponents, we know we will generate fractions; however, if a fraction is raised by a negative integer exponent, our answer will be whole number instead.

For example: 

\(\displaystyle \frac{1}{2}^{-2}=\frac{1}{\frac{1}{2^2}}=\frac{1}{\frac{1}{4}}=4\)

The following rule has been used in this scenario:

\(\displaystyle x^{-a}=\frac{1}{x^a}\) 

In this formula, \(\displaystyle a\) is a positive exponent raising the base \(\displaystyle x\).

We know \(\displaystyle 256=16^2\).

Since we are dealing with a integer and converting to fractional base, we know we need to have a negative exponent.

The answer is:

\(\displaystyle \frac{1}{16}^{-2}\)

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

\(\displaystyle 18^8=18*18*18*18*18*18*18*18\)

When expanding an exponent, we must multiply the base by itself for the number of indicated by the exponential value.

\(\displaystyle 15^3\) is expanded out to the following:

\(\displaystyle 15*15*15\)

The product is \(\displaystyle 3375\).

First, we know that \(\displaystyle 8=2^3\).

Apply the power rule of exponents:

\(\displaystyle (a^m)^n=a^m^n\)

We can then write the following expression:

 \(\displaystyle (2^3)^{12}=2^{36}\)

Second, we know that \(\displaystyle 4=2^2\). 

By applying the same rule, we will get the following expression:

\(\displaystyle (2^2)^x=2^{36}\)

Therefore:

\(\displaystyle 2x=36\) and \(\displaystyle x=18\) 

The answer is \(\displaystyle 4^{18}\).

First, we know that \(\displaystyle 27=3^3\).

Apply the power rule of exponents:

\(\displaystyle (a^m)^n=a^m^n\)

We can then write the following expression:

\(\displaystyle (3^3)^6\) or \(\displaystyle 3^{18}\)

First, we know that \(\displaystyle 8=2^3\).

Apply the power rule of exponents:

\(\displaystyle (a^m)^n=a^m^n\)

We can then write the following expression:

\(\displaystyle (2^3)^{12}=2^{36}\)

First, we know that \(\displaystyle 16=2^4\).

Apply the power rule of exponents:

\(\displaystyle (a^m)^n=a^m^n\)

We can then write the following expression:

 \(\displaystyle (2^4)^{9}=2^{36}\)

Second, we know that \(\displaystyle 8=2^3\). 

By applying the same rule, we will get the following expression:

\(\displaystyle (2^3)^x=2^{36}\)

Therefore:

\(\displaystyle 3x=36\)

Simplify and solve for \(\displaystyle x\).

\(\displaystyle x=12\)

The answer is \(\displaystyle 8^{12}\).

When expanding exponents, we repeat the base by the exponential value.

\(\displaystyle 11^4=11*11*11*11\)

When expanding exponents, we repeat the base by the exponential value.

\(\displaystyle 2^7=\)\(\displaystyle 2*2*2*2*2*2*2\)