The power rule of exponents states that when an exponential term is raised to another power, we multiply the exponents to simplify.

\(\displaystyle (2^{4})^{6}=2^{4*6}=2^{24}\)

The power rule says that an exponent to the power of another exponent gets multiplied.  We can think of \(\displaystyle (X^2)^4\) as \(\displaystyle X^2 \times X^2 \times X^2 \times X^2\), in which case we see that the answer is \(\displaystyle X^8\) because multiplying the same numbers with different exponents adds the exponents.

When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.

If you think about it \(\displaystyle (x^{4})^{3}\)is equivalent to \(\displaystyle (x*x*x*x)(x*x*x*x)(x*x*x*x)\)

So we multiply \(\displaystyle 4\) by \(\displaystyle 3\) to get the power of the answer \(\displaystyle 12\)

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

The power rule of exponents states than an exponential term raised to another exponent can be simplified by multiplying the exponents together.

\(\displaystyle (y^4)^5\)

\(\displaystyle (y)^{4*5}\)

\(\displaystyle y^{20}\)

When raising a polynomial to a power you multiply the polynomial inside the parentheses by the power outside of the parentheses.

So we multiply \(\displaystyle 6\) by \(\displaystyle 8\) to get the power of the answer as \(\displaystyle 48\).

The answer is \(\displaystyle x^{48}\).

When raising a polynomial to a power, you multiply the exponent inside the parentheses by the power outside of the parentheses.

So we multiply \(\displaystyle 5\) by \(\displaystyle 9\) to get the power of the answer, which is \(\displaystyle 45\).

The answer is \(\displaystyle x^{45}\).

Exponents are a way of expressing the repeated multiplication of the same value. An exponent describes how many times a value is to be multiplied by itself.

\(\displaystyle 9^{3}=9\cdot 9\cdot 9=729\)

You can simplify negative exponents in order to work only with positive numbers. Simply make the negative number positive and divide 1 by the entire expression.

\(\displaystyle 4^{-3}=1/4^{3}\)

When raising an exponent to another exponent you multiply the exponent inside the parentheses by the exponent outside of the parentheses.

So we multiply \(\displaystyle 5\) by \(\displaystyle 12\) to get the final exponent, which is \(\displaystyle 60\).

The answer is \(\displaystyle x^{60}\).

When raising a polynomial to a power, multiply the polynomial inside the parentheses by the power outside of the parentheses.

We multiply \(\displaystyle 5\) by \(\displaystyle 4\) to get the power of the answer, \(\displaystyle 20\).

The answer is \(\displaystyle x^{20}\).